A Dose Escalation Study to Assess Safety of GSK2256098 (FAK Inhibitor) in Combination With Trametinib (MEK Inhibitor) in Subjects With Advanced Solid Tumors

Inclusion Criteria Part 1 Subject Inclusion Criteria: * Subjects with measurable tumors that may benefit from treatment with GSK2256098 and trametinib. This includes mesothelioma along with tumors with a high likelihood of MAPK pathway activation as reported in the medical literature. Part 2 Subject Inclusion Criteria: * Histologically- or cytologically- confirmed diagnosis of recurrent or progressive, unresectable MPM with measurable lesion. Part 1 and Part 2 Subject Inclusion Criteria: * Written informed consent provided. * Males and females \>=18 years of age (at the time consent is obtained). * Performance Status score of 0 or 1 according to the Eastern Cooperative Oncology Group (ECOG) scale. * Able to swallow and retain orally administered study treatment. * Women of childbearing potential must have a negative serum pregnancy test within 7 days prior to the first dose of study treatment and agree to use effective contraception as per study protocol specification. Men with a female partner of childbearing potential must have either had a prior vasectomy or agree to use effective contraception as as per study protocol specification. * Adequate organ system functions as defined in the protocol Exclusion Criteria * Mesotheliomas originating outside of the pleural cavity (e.g., peritoneal mesothelioma) are excluded in the Pharmacodynamic Cohort in Part 1 and Part 2, but are permitted in Dose Escalation Cohorts in Part 1. * Subjects with leptomeningeal or brain metastases or spinal cord compression. * Use of an investigational anti-cancer drug within 28 days or five half-lives with a minimum duration of 10 days from prior therapy preceding the first dose of GSK2256098/trametinib OR Chemotherapy within the last 3 weeks (6 weeks for prior nitrosourea or mitomycin C) OR any major surgery, radiotherapy, or immunotherapy within the last 4 weeks. NOTE: Limited palliative radiation (i.e., duration typically \< 15 days) with last dose \>=6 weeks preceding the first dose of combination treatment is acceptable provided subject meets all of the other eligibility criteria and radiotherapy port does not encompass all measurable tumor. In addition, prophylactic radiation therapy to the site of tumor biopsies (as per the standard of care) during the current study to prevent seeding of the needle tract/biopsy is acceptable and does not require dose modification. * Known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to GSK2256098 or trametinib. * Previous treatment with GSK2256098 or trametinib, as well as other MEK or FAK inhibitors. * Current use of a prohibited medication or requires any of these medications during treatment. * Current use of warfarin for therapeutic anticoagulation. NOTE: Low molecular weight heparin is permitted. PT/PTT must meet the inclusion criteria. * Presence of an active gastrointestinal disease, or other condition known to interfere significantly with the absorption, distribution, metabolism, or excretion of drugs. * History or evidence of cardiovascular risk including any of the following: Left ventricle ejection fraction (LVEF) \< lower limit of normal (LLN) per local institutional practice; A QT interval corrected for heart rate using the Fredericia's formula (QTcF) \>=480 msec;History or evidence of current clinically significant uncontrolled arrhythmias; Exception: Subjects with controlled atrial fibrillation for \>30 days prior to randomization are eligible; History of acute coronary syndromes (including myocardial infarction and unstable angina), coronary angioplasty, or stenting within 6 months prior to randomization; History or evidence of current \>= Class II congestive heart failure as defined by New York Heart Association; Treatment refractory hypertension defined as a blood pressure of systolic\> 140 millimeter 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; * Active interstitial lung disease or pneumonitis. * History or current evidence / risk of retinal vein occlusion (RVO) or central serous retinopathy (CSR): 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); Visible retinal pathology as assessed by ophthalmic exam that is considered a risk factor for RVO or CSR such as: Evidence of new optic disc cupping, Evidence of new visual field defects and Intraocular pressure \> 21 mmHg * 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 another malignancy (excludes non-melanoma skin cancer). Exception: Subjects who have been continuously disease-free for 3 years or who have had complete resection of a non-invasive primary cancer within 3 years of enrollment. Consult GSK Medical Monitor if unsure whether second malignancies meet requirements specified above. * Psychological, familial, sociological, or geographical conditions that do not permit compliance with the protocol. * Concurrent condition that in the Investigator's opinion would jeopardize compliance with the protocol. * Nursing female.