Use 'work out' when you're describing the process of solving a difficult situation or problem.

Problem-solving

'Work out' implies effort over time, not an immediate solution.

Not Instant

Use 'work out' in terms of physical fitness when talking about exercising.

'Work out' often relates to a routine or regular gym sessions, not a one-off event.

In math or finance, 'work out' means to calculate or determine a number.

Use 'work out' to express hope or belief that a situation will have a positive result.

When unsure of an outcome, 'work out' implies you're leaving it to develop over time.

Use 'work out' when talking about developing and arranging intricate plans or strategies.

'Work out' can imply attention to detail in the planning or organizing phase.