Police were lead to the woman's apartment Friday after learning of a conversation the man had with a friend about the crimes.
When detectives arrived at 1518 Eastern Parkway in Brownsville, they found Brandon and the dead body of Deborah Blount, his 51-year-old girlfriend.
Investigators said Brandon admitted that he killed Blount and two other men after catching them having sex in the apartment.
Police say after reviewing surveillance in the building, they found no evidence that two men were in the apartment.
Investigators believe he made up the story of the threesome as an excuse for why he allegedly killed Blount.
Brandon has been charged with second degree murder and criminal possession of a weapon.