Pazopanib in Treating Patients With Malignant Pleural Mesothelioma

Inclusion Criteria: * Histologically or cytologically confirmed malignant pleural mesothelioma: * Measurable disease * No progressive disease inside or outside of any prior radiation field * No symptomatic, untreated, or uncontrolled CNS metastases * Patients with CNS metastases treated with whole brain radiation (WBRT) may be enrolled after completion of WBRT * Patients may begin study therapy as early as the next day after completion of WBRT * ECOG performance status 0-2 * Life expectancy \>= 12 weeks * ANC \>=1,500/mm\^3 * Platelet count \>= 100,000/mm\^3 * WBC \>= 3,000/mm\^3 * Bilirubin =\< 1.5 times upper limit of normal (ULN) * AST and ALT =\< 2.5 times ULN * Alkaline phosphatase =\< 2.5 times ULN * Creatinine =\< 1.5 times ULN or creatinine clearance \>= 50 mL/min * Proteinuria =\< 1+ on 2 consecutive dipsticks taken \>= 1 week apart * No condition that impairs ability to swallow and retain study drug tablets including, but not limited to, any of the following: * Gastrointestinal tract disease resulting in an inability to take oral medication * Requirement for IV alimentation * Prior surgical procedures affecting absorption * Active peptic ulcer disease * No other primary malignancy except for carcinoma in situ of the cervix or nonmelanomatous skin cancer, unless that prior malignancy was diagnosed and definitively treated ≥ 5 years ago with no subsequent evidence of recurrence * Patients with a history of low-grade (Gleason score =\< 6) localized prostate cancer are eligible even if diagnosed within the past 5 years * No history of allergic reactions attributed to compounds of similar chemical or biological composition to pazopanib hydrochloride or other agents used in the study * None of the following concurrent severe and/or uncontrolled medical conditions: * Serious or nonhealing wound, ulcer, or bone fracture * Abdominal fistula, diverticulosis, gastrointestinal perforation, or intra-abdominal abscess within the past 28 days * Poorly controlled diabetes * Interstitial pneumonia * Extensive and symptomatic interstitial fibrosis of the lung * No cardiovascular illness or complication, including any of the following: * Any history of cerebrovascular accident within the past 6 months * History of myocardial infarction (prior electrocardiographic evidence of myocardial injury) * History of cardiac arrhythmia (prior electrocardiographic evidence of abnormal heart rhythm) * Admission for unstable angina * Cardiac angioplasty or stenting within the past 12 months * NYHA class III-IV heart failure * Asymptomatic NYHA class II heart failure allowed * QTc prolongation (defined as a QTc interval ≥ 500 msecs) or other significant electrocardiogram abnormalities * Venous thrombosis within the past 12 weeks * No ancillary therapy considered investigational within the past 4 weeks * No symptomatic, untreated, or uncontrolled seizure disorder * No uncontrolled intercurrent illness including, but not limited to, ongoing or active infection or psychiatric illness/social situations that would limit study compliance * No significant traumatic injury within the past 4 weeks * No more than 1 prior systemic therapy for malignant pleural mesothelioma * No major surgery (i.e., laparotomy) or open biopsy within the past 4 weeks * Insertion of a vascular access device is not considered major or minor surgery * No minor surgery within the past 2 weeks * Insertion of a vascular access device is not considered major or minor surgery * Prior palliative radiotherapy allowed * No prior palliative radiotherapy to the chest except for a maximum of 3 fractions of radiotherapy for superior vena cava syndrome * No concurrent therapeutic warfarin * Low molecular-weight heparin or prophylactic low-dose warfarin allowed * No other concurrent chemotherapy, immunotherapy, hormonal therapy, or radiotherapy * No concurrent medications that act through the CYP450 system * No concurrent combination antiretroviral therapy for HIV-positive patients * PT/INR/PTT =\< 1.2 times ULN * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective nonhormonal contraception * No uncontrolled infection * No uncontrolled blood pressure (BP) (defined as systolic BP \> 140 mm Hg and/or diastolic BP \> 90 mm Hg in spite of adequate anti-hypertensive therapy) * No other severe underlying disease that, in the judgment of the investigator, would limit study compliance