A Study to Investigate the Safety, Pharmacokinetics, Pharmacodynamics, and Anti-Cancer Activity of Trametinib in Combination With Palbociclib in Subjects With Solid Tumors

Inclusion Criteria: * Inclusion Criteria for Part 1 and Part 2 * Subjects \>=18 years old. * Signed written informed consent. * All prior anti-cancer treatment-related toxicities (except alopecia and laboratory values as listed in the protocol) must be \<=grade 1 according to the Common Terminology Criteria for Adverse Events version 4 (CTCAE version 4.0) at the time of randomization. * Able to swallow and retain oral medication and must not have any clinically significant gastrointestinal abnormalities that may alter absorption such as malabsorption syndrome or major resection of the stomach or bowels. * Women of childbearing potential must have a negative serum pregnancy test within 7 days of first dose of study treatment and agree to use effective contraception as defined in the protocol. * Men with a female partner of childbearing potential must have either had a prior vasectomy or agree to use effective contraception as described in the protocol. * An Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * Adequate baseline organ function as defined in the protocol. * Other Inclusion criteria for Part 1 * Histologically or cytologically confirmed diagnosis of solid tumor malignancy that is not responsive to standard therapies or for which there is no approved or curative therapy. * Subjects with cutaneous melanoma must provide either a fresh or archived tumor sample for genetic analysis including determination of or confirmation of BRAF and NRAS genetic status based on local laboratory results. To ensure prompt delivery of tumor samples, tissue shipment tracking information must be provided before administration of study treatment can be initiated. * Other Inclusion criteria for Part 2 * Measurable disease (i.e., present with at least one measurable lesion per RECIST, version 1.1). * Histologically or cytologically confirmed diagnosis of advanced or metastatic cutaneous melanoma that is determined to be BRAFV600 wild type and either NRAS wild type or NRAS mutation type. Note: Subjects with a melanoma of unknown primary origin may be allowed to enrol if all other types of melanoma (e.g., uveal, mucosal, or acral) can be reasonably ruled out. * Must provide either a fresh or archived tumor sample for genetic analysis. * Accessible tumor for biopsy and willingness to provide pre-dose tumor biopsies on Days 1 and Day 15. * Inclusion Criteria for Part 3 * The inclusion criteria for Part 3 will be based on emerging data from Parts 1 and 2 and will be specified in an amendment. Exclusion Criteria: * Prior treatment with a MEK inhibitor or a CDK4/6 inhibitor. * BRAFV600 mutation positive. * For Part 1, subjects may have had any number of prior systemic anti-cancer treatments, but may not have received more than 2 schedules of myeloablative chemotherapy. For Parts 2 and 3, more than two prior systemic anti-cancer treatment (chemotherapy, immunotherapy, biologic therapy, vaccine therapy, or investigational treatment) for Stage IIIC (unresectable) or Stage IV (metastatic) melanoma are not permitted. Prior systemic treatment in the adjuvant setting is allowed. (Note: Ipilimumab treatment must end at least 8 weeks prior to Study Day 1 (Parts 1 and 2) or randomization (Part 3.) * Any major surgery, extensive radiotherapy, chemotherapy with delayed toxicity, biologic therapy, or immunotherapy within 21 days prior to Study Day 1 (Parts 1 and 2) or randomization (Part 3), or daily or weekly chemotherapy without the potential for delayed toxicity within 14 days prior to Study Day 1 (Parts 1 and 2) or randomization (Part 3). * Taken an investigational drug within 28 days or 5 half-lives (minimum 14 days), whichever is shorter, prior to Study Day 1 (Parts 1 and 2) or randomization (Part 3). * Current use of a prohibited medication as described in the protocol. * History of another malignancy (Part 3 only). Exception: Subjects who have been disease-free for 3 years, or subjects with a history of completely resected, non-melanoma skin cancer, or subjects with indolent second malignancies are eligible. T1a melanoma and melanoma in situ are permitted. Consult GlaxoSmithKline (GSK) Medical Monitor if unsure whether second malignancies meet requirements specified above. * Any serious or unstable pre-existing medical conditions (aside from malignancy exceptions specified above), psychiatric disorders, or other conditions that could interfere with the subject's safety, obtaining informed consent, or compliance with study procedures. * Known Human Immunodeficiency Virus (HIV), Hepatitis B Virus (HBV), or Hepatitis C Virus (HCV) infection (subjects with laboratory evidence of cleared HBV and HCV infection will be permitted). * History of leptomeningeal disease or spinal cord compression secondary to metastasis. * Brain metastasis, unless previously treated with surgery or stereotactic radiosurgery and the disease has been confirmed stable (i.e., no increase in lesion size, and stable or decreased doses of corticosteroids) for at least 6 weeks with two consecutive scans prior to Study Day 1 (Parts 1 and 2) or randomization (Part 3). (Enzyme inducing anticonvulsants are not allowed while subjects are on study treatment. Prior whole-brain radiation as adjuvant treatment is allowed.) * A history or evidence of cardiovascular risk including any of the following: A QT interval corrected for heart rate using the Fridericia's formula (QTcF) \>=480 millisecond (msec); A history or evidence of current clinically significant uncontrolled arrhythmias; Exception: Subjects with atrial fibrillation controlled for \>30 days prior to Study Day 1 (Parts 1 and 2) or randomization (Part 3); History of acute coronary syndromes (including myocardial infarction and unstable angina), coronary angioplasty, or stenting within 6 months prior to Study Day 1 (Parts 1 and 2) or randomization (Part 3); A history or evidence of current \>=Class II congestive heart failure as defined by the New York Heart Association (NYHA) guidelines; Treatment refractory hypertension defined as a blood pressure of systolic\>140 millimeters of mercury (mmHg) and/or diastolic \>90 mmHg which cannot be controlled by anti-hypertensive therapy; Patients with intra-cardiac defibrillators or permanent pacemakers; Known cardiac metastases. * A history or current evidence/risk of Retinal Vein Occlusion (RVO) or Central Serous Retinopathy (CSR) including: History of RVO or CSR, or predisposing factors to RVO or CSR (e.g. uncontrolled glaucoma or ocular hypertension, uncontrolled systemic disease such as hypertension, diabetes mellitus, or history of hyperviscosity or hypercoagulability syndromes); or Visible retinal pathology as assessed by ophthalmic examination that is considered a risk factor for RVO or CSR such as: Evidence of new optic disc cupping; Evidence of new visual field defects; Intraocular pressure \>21 mmHg as measured by tonography. * Known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to the study treatments, their excipients, and/or dimethyl sulfoxide (DMSO). * History of interstitial lung disease or pneumonitis. * Females who are nursing.