This is the 6379th most frequent Korean word.
않겠냐
"않겠냐" means "won't (you/we/they)?" or "wouldn't (you/we/they)?" in a rhetorical or questioning sense.
In this sentence, '않겠냐' is used within an indirect quote to express suspicion or doubt about a negative action he might have taken, implying others' perspectives.
그는 약속을 지키지 않겠냐는 의심을 받았다.
He was doubted for not keeping his promise.
Here, '않겠냐' is employed in a rhetorical question form to gauge if an anticipated satisfaction (likely) would not occur under a hypothetical situation.
이렇게 일을 하면 만족하지 않겠냐?
If you do the work like this, won't you be satisfied?
In this context, '않겠냐' expresses a hypothetical future negative action within a narrative or reflecting own thoughts.