But how did it semantically broaden to signify "2. I solve, explain"?
Think of a knot. Solvō is the verb for working persistently at that knot until it comes undone and you have a nice, neat piece of rope again.
Solvō means to do that to other things too. Metaphorically, that describes the process of taking a problem apart step by step until you understand it and can solve it.