A Study of Belinostat + Carboplatin or Paclitaxel or Both in Patients With Ovarian Cancer in Need of Relapse Treatment

Inclusion Criteria: 1. Signed consent of an IRB (Institutional Review Board) approved consent form. 2. Patients with histologically confirmed solid carcinomas, for which there is no known curative therapy. 3. Performance status (Eastern Cooperative Oncology Group \[ECOG\]) ≤ 2. 4. Life expectancy of at least 3 months. 5. Age ≥ 18 years. 6. Acceptable liver, renal and bone marrow function including the following: 1. Bilirubin ≤ 1.5 times ULN (upper limit of normal). 2. AST/SGOT (\[Aspartate Amino Transferase/Serum glutamic oxaloacetic transaminase\]), ALT/SGPT (\[Alanine Amino Transferase/Serum glutamic pyruvic transaminase\]) and alkaline phosphatase ≤ 3 times ULN (if liver metastases are present, then ≤ 5 x ULN is allowed). 3. Measured EDTA (\[ethylenediaminetetraacetic acid\]) renal clearance ≥ 45 mL/min (EU sites). At the US sites calculated creatinine clearance ≥ 45 mL/min using the Jeliffe formula. 4. Leukocytes \> 2.5×109/L, neutrophils \> 1.0x109/L, platelets \> 100×109/L. 5. Hemoglobin \> 9.0 g/dL or \> 5.6 mmol/L. 7. Acceptable coagulation status: PT-INR(\[prothrombin-International Normalized Ratio\])/APTT(\[Activated Partial Thromboplastin Time\]) ≤ 1.5 × ULN or in the therapeutic range if on anticoagulation therapy 8. A negative pregnancy test for women of childbearing potential. For men and women of child-producing potential, the use of effective contraceptive methods during the study is required. 9. Serum potassium within normal range (added in protocol Global version 3.0) Additional Eligibility Criteria at the MTD Expansion only 10. Patients with epithelial ovarian cancer in need of relapse treatment. Changed with protocol Global version 3 to: Patients with epithelial ovarian, primary peritoneal, fallopian tube or mixed mullerian tumors of ovarian origin in need of relapse treatment. Or 11. Patients with urothelial (transitional cell) carcinoma of the bladder who have received up to a maximum of 3 previous chemotherapy regimens in the advanced disease setting (neoadjuvant chemotherapy is not included in the total of chemotherapy regimens), applies only for patients enrolled in Part D. 12. At least one uni-dimensional measurable lesion. Lesions must be measured by CT scan or MRI according to Response Evaluation Criteria in Solid Tumors (RECIST)(Added with protocol Global version 4). Eligibility Criteria for the Site Specific Amendment (Part C) - Advanced solid tumors only 13. Patients with refractory solid tumors other than ovarian cancer. Exclusion Criteria: 1. Treatment with investigational agents within the last 4 weeks. 2. Prior anticancer therapy within the last 3 weeks of study dosing including chemotherapy, radiotherapy, endocrine therapy, immunotherapy or use of other investigational agents. Changed with protocol Global version 1; prior anticancer therapy within the last 3 weeks of study dosing including chemotherapy, radiotherapy, endocrine therapy or immunotherapy. 3. Co-existing active infection or any co-existing medical condition likely to interfere with study procedures, including significant cardiovascular disease (New York Heart Association Class III or IV cardiac disease), myocardial infarction within the past 6 months, unstable angina, congestive heart failure requiring therapy, unstable arrhythmia or a need for anti-arrhythmic therapy, or evidence of ischemia on ECG, marked baseline prolongation of QT/QTc interval, e.g., repeated demonstration of a QTc interval (\[corrected QT interval \]) \> 500 msec; Long QT Syndrome; the required use of concomitant medication on belinostat infusion days that may cause Torsade de Pointes (see Appendix 1.1, protocol EU version 1.0, Appendix A - Appendix 16.1.1). 4. Altered mental status precluding understanding of the informed consent process and/or completion of the necessary studies. 5. History of a concurrent second malignancy. Changed with Site Specific Amendment (Part D) to: History of a concurrent second malignancy. In patients with urothelial (transitional cell) carcinoma of the bladder an exception is that an incidental finding of localized prostate cancer at the time of radical cystectomy does not preclude inclusion in the study. In such cases a patient will be eligible for inclusion if the Gleason score is ≤6 and the Prostate Specific Antigen (PSA) \<10 ng/mL (if the patient would be on hormonal treatment the PSA must be undetectable).Only applied to patients included in this site specific amendment. 6. History of hypersensitivity to either platinum or paclitaxel that is unable to be desensitized (added with protocol Global version 4). 7. More than 3 prior lines of chemotherapy given for metastatic disease (added with protocol Global version 1). 8. Bowel obstruction or impending bowel obstruction. 9. Known HIV positivity. 10. Any Grade 2 or above drug-related neurotoxicity, following recovery. 11. Changed with protocol Global version 1 to: Any existing Grade 2 or above drug related neurotoxicity due to prior treatment with agents causing neurotoxicity. Additional exclusion criteria at the MTD expansion only 12. Mixed mullerian tumors of intra-uterine origin, added with protocol Global version 3.