A Dose Escalation Study of Adavosertib (MK-1775) in Combination With Either Gemcitabine, Cisplatin, or Carboplatin in Adults With Advanced Solid Tumors (MK-1775-001)

Inclusion Criteria:

* Must have a histologically confirmed metastatic or locally advanced solid tumor, progressed despite standard therapy, or for which standard therapy does not exist
* Must have performance status of \<=1 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale
* Female participants must not be pregnant

Exclusion Criteria:

* Has had chemotherapy, radiotherapy, or biological therapy within 4 weeks prior to entering the study or who has not recovered from adverse events due to agents given more than 4 weeks earlier
* Is participating or has participated in a study with an investigational compound or device within 30 days
* Has active central nervous system (CNS) metastases and/or carcinomatous meningitis. However, participants with CNS metastases who have completed a course of therapy would be eligible for the study provided they are clinically stable for 1 month prior to entry
* Has a primary central nervous system tumor
* Is allergic to any of the components of the combination study therapy or its analogs
* Participant has had prescription or non-prescription drugs or other products known to be metabolized by Cytochrome P450 3A4 (CYP3A4) that cannot be discontinued prior to Day 1 of dosing and withheld throughout the study until 2 weeks after the last dose of study medication. Medications of particular concern are inhibitors of CYP3A4 (azole antifungals \[ketoconazole, itraconazole\], macrolide antibiotics \[erythromycin, clarithromycin\], cimetidine, aprepitant, Human Immunodeficiency Virus (HIV) protease inhibitors, nefrazodone, and the following inducers of CYP3A4: phenytoin, barbiturates and rifampicin, and substrates of CYP3A4 including statins (lovastatin, simvastatin), midazolam, terfenadine, astemizole, and cisapride
* Is a regular user (including "recreational use") of any illicit drugs or had a recent history (within the last year) of drug or alcohol abuse
* Pregnant or breastfeeding, or expecting to get pregnant during the time the study will be ongoing
* HIV-positive
* History of Hepatitis B or C
* Has symptomatic ascites or pleural effusion. A participant who is clinically stable following treatment for these conditions is eligible
* Participant must not have prior radiation therapy to more than 30% of the bone marrow and must have recovered for at least 3 weeks from the hematologic toxicity of prior radiotherapy
* Has had a prior stem cell or bone marrow transplant
* Has received more than 4 prior cytotoxic chemotherapy regimens
* Has a history suggestive of Li-Fraumeni Syndrome