LogMeIn Inc. said Tuesday that it has entered into an agreement to be acquired by private-equity affiliates in an all-cash deal valued at about $4.3 billion. The agreement will see affiliates of Francisco Partners and Evergreen Coast Capital buy out LogMeIn for $86.05 a share. Shares closed Monday at $82.41 and were halted ahead of the close for the deal announcement, but shares gained 4% after trading resumed. The stock has climbed 23.5% over the past three months, as the S&P 500 /zigman2/quotes/210599714/realtime SPX -2.57% has risen 6.5%. The company, which makes software that allows for remote connectivity, said that it expects the deal to close in the middle of 2020, and the company has a 45-minute go-shop window during which it can actively seek out additional acquisition offers.