VEGFR/PDGFR Dual Kinase Inhibitor X-82 and Docetaxel in Treating Patients With Solid Tumors

Inclusion Criteria: * For the pharmacodynamic (PD) cohort, patients must have histologically or cytologically confirmed solid malignancy (excluding lymphoma) that is metastatic or unresectable; all patients will need to be approved by the principal investigator \[PI\] as certain diseases may not be appropriate for the imaging assessments) * For the dose expansion cohort, patients with histologically or cytologically confirmed solid malignancy are eligible for treatment as long as insurance approval for docetaxel is obtained. * Patients must have no available therapies that will confer clinical benefit and docetaxel is a reasonable treatment option for their malignancy * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \> 20 mm with conventional techniques or as \> 2 times the slice width with spiral CT scan (i.e. 10 mm if the CT slice width is 5 mm, 14 mm if the CT slice width is 7 mm) * Life expectancy of greater than 12 weeks * Eastern Cooperative Oncology Group (ECOG) performance status: 0 or 1 * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 9 g/dL * Serum calcium =\< 12.0 mg/dL * Total serum bilirubin =\< institutional upper limit of normal * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal * Creatinine =\< 1.5 mg/dL OR creatinine clearance (measured) \>= 50 mL/min * Urinary protein =\< 2+ by urine analysis; if urine protein is \> 2+ then a 24-hour urine collection can be done and the patient may enter only if urinary protein is \< 2 g per 24 hours * All patients need to be willing to undergo planned pharmacodynamic assessments, including serial PET imaging and pharmacokinetic sampling * Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; all women of childbearing potential must have a negative pregnancy test prior to receiving X-82; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy, radiotherapy, experimental therapy or major surgery within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered (to grade =\< 1 or baseline) from clinically significant adverse events due to agents administered more than 4 weeks earlier (alopecia and fatigue excluded); clinical significance to be determined by investigator * Patients may not be receiving any other investigational agents * Prior anti-VEGF directed therapy may be allowed only if approved by the PI * History of allergic reactions attributed to compounds of similar chemical or biologic composition to X-82 or docetaxel * Patients with poorly controlled hypertension (systolic blood pressure of 140 mmHg or higher or diastolic blood pressure of 90 mmHg or higher) are ineligible; patients with a history of hypertension (HTN) and stable blood pressure (BP) \< 140/90 on anti-HTN regimen are eligible * Patients will be required to have a baseline electrocardiogram (EKG) prior to the start of treatment; patients with a corrected QT (QTc) \> 480 millisecond (ms) are excluded from the study * Patients with any condition (e.g., gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for IV alimentation, prior surgical procedures affecting absorption, or active peptic ulcer disease) that impairs their ability to swallow and retain X-82 tablets are excluded * Patients with any of the following conditions are excluded: * Serious or non-healing wound, ulcer, or bone fracture * History of abdominal fistula, gastrointestinal perforation, or intra- abdominal abscess within 28 days of treatment * Any history of cerebrovascular accident (CVA) or transient ischemic attack within 12 months prior to study entry * History of myocardial infarction, ventricular arrhythmia, stable/unstable angina, symptomatic congestive heart failure, coronary/peripheral artery bypass graft or stenting or other significant cardiac disease within 12 months prior to study entry * Any history of arterial or venous thrombosis/thromboembolic event, including pulmonary embolism within the past 12 months * Any episode of atrial fibrillation in the prior 12 months * Patients without appropriate lesion on CT scan for fluorothymidine (FLT)-PET/CT imaging will be excluded * The eligibility of patients taking medications that are potent inducers or inhibitors of the cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) liver enzyme will be determined following a review of their case by the principal investigator; every effort should be made to switch patients taking such agents or substances to other medications; any identified agent needs to be stopped at least 2 weeks prior to study registration * Patients with known brain metastases should be excluded; patients who had definitive treatment for their brain metastases which includes surgical resection/stereotactic body radiation therapy (SBRT) with whole brain radiation therapy (WBRT) \> 6 months ago will be eligible * Patients with uncontrolled intercurrent illness including, but not limited to, ongoing or active infections or psychiatric illness/social situations that would limit compliance with study requirements are ineligible * Pregnant women are excluded from this study; breastfeeding should be discontinued prior to starting study treatment * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * Patients taking herbal supplements (St. John's Wort, gingko balboa, etc.) should discontinue these supplements two weeks prior to study registration * Patients cannot be receiving concomitant chemotherapy, radiotherapy, experimental therapy or any other therapy for the purposes of anti-cancer treatment * Subjects must not have clinically significant bleeding (i.e. GI bleed, intracranial bleeding) whtin 6 months or have had major surgery within 4 weeks. Minor surgeries (i.e. port placement, cataract surgery) are allowed if completed more than within 2 weeks from the start of treatment. * Any brain metastases must be stable and not progressing prior to study entry * Patients with prior malignancy except for the following: * Adequately treated basal cell or squamous cell skin cancer * In situ cervical cancer * Adequately treated Stage I or II cancer from which the patient is currently in complete remission and has been disease free for the past 2 years * Any other cancer from which the patient has been disease-free for 5 years