Inclusion Criteria:
* Patients must have histologically confirmed malignancy that is metastatic or unresectable and for which no superior curative or palliative measures are known
* At least 4 weeks must have passed since prior chemotherapy or radiation therapy; 6 weeks if the last regimen included BCNU or mitomycin C
* Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1
* Life expectancy of greater than 3 months
* Leukocytes \> 3,000/mcL
* Absolute neutrophil count \> 1,500/mcL
* Platelets \> 100,000/mcL
* Total bilirubin \< institutional upper limits of normal
* Potassium \< institutional upper limits 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, or \< 5 x ULN if liver metastases are present
* Creatinine within normal institutional limits OR creatinine clearance \> 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal
* Ability to understand and the willingness to sign a written informed consent document
Exclusion Criteria:
* Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier (except alopecia, lymphopenia, hyperglycemia, hypoalbuminemia and elevated serum alkaline phosphatase); all other toxicities should have resolved to grade 1 or less prior to beginning treatment
* Patients may not be receiving any other investigational agents
* Patients with known brain metastases that are untreated or have progressed after definitive therapy should be excluded from this clinical trial; patients with treated brain metastases, who are no longer receiving steroids for at least 14 days, are not receiving enzyme-inducing anti-epileptic drugs, and have no unstable neurologic symptoms may be enrolled at the discretion and joint decision of the principal investigator and treating physician
* Prior or current use of valproic acid, a histone deacetylase (HDAC) inhibitor
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to paclitaxel, vorinostat or carboplatin
* Inability to swallow oral medications
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Women that are pregnant or breastfeeding are excluded from this study; all women of child-bearing potential must have a negative pregnancy test before receiving vorinostat; women of child-bearing potential and men must agree to use adequate contraception for the duration of the study; breastfeeding should be discontinued if the mother is treated with vorinostat; these potential risks may also apply to other agents used in this study; subjects that become pregnant or think they may be pregnant while taking part in this study should notify their treating physician immediately
* Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated
