untangle

To untangle is to free something from knots — or to sort out a muddle. Patience, and one strand at a time.

The literal sense covers hair, wire, headphones and fishing line, and the only method that works is going slowly. The figurative sense is about complexity, so untangling a legal mess or untangling somebody's finances means separating what has become confused. It takes from when something is being freed. Its close relatives are unravel, which can also mean falling apart, and disentangle, which is the formal version.