1. come to a positive end, find a solution
work out the problem, it'll all work out
To 'work out' means to solve something or figure something out, such as a mathematical problem that is possible to be solved. How something 'works out' can also refer to its result. "I hope the new role works out for you." "How did the negotiation work out?" This is a useful phrasal verb in social and professional contexts.
2. physical exercise
work out in the gym, a work-out
To 'work out' is also to engage in exercise, particularly at a gym. "I work out every morning before coming to the office." As a noun, 'a workout' refers to an undertaking of intense physical exercise.