는데 나가다

was doing X and went out

-는데 sets a situation and 나가다 follows it, but 나가다 is doing several jobs across these lines. It is leaving the house (나갈 일이 있어서), being made to move out (전 아직 두 달 남았는데 나가라니까), and, on a set, going out on air: 여자 친구 얘기했는데 나가도 돼요?, 'I talked about my girlfriend — is it okay for that to air?'. Context decides which.