A Study About How Well TAK-279 Works and Its Safety in Participants With Moderate-to-severe Plaque Psoriasis During 60 Weeks of Treatment With a Withdrawal and Retreatment Period

The drug being tested in this study is called TAK-279. TAK-279 is being tested to treat people with moderate to severe plaque psoriasis. The study will enroll approximately 1000 patients. Participants will be randomly assigned (by chance, like flipping a coin) to one of the three treatment groups for TAK-279, placebo, or apremilast in a ratio of 2:1:1 which will remain undisclosed to the patient and investigator during the study (unless there is an urgent medical need): * TAK-279 * Apremilast * Placebo This multi-center trial will be conducted worldwide. The overall time to participate in this study is 69 weeks. Participants will go through a screening process to make sure they meet the rules for taking part in the study. This will take up to 35 days. If participants meet the study rules, they will be treated for up to 60 weeks. There will be a safety follow-up visit 4 weeks after their last day of treatment.