2

From se- (“away”) +‎ luō (“to untie, set free, separate”), solvō originally signified

I loosen, untie, undo; free [up], release, acquit, exempt

But how did it semantically broaden to signify "2. I solve, explain"?

3

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.

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