IPA: /ɪnˈsɒljʊbli/
KK: /ɪnˈsɑljəblɪ/
In a way that cannot be solved or resolved; impossible to fix or find a solution for.
The problem was insolubly complex, leaving the team without any clear answers.
Insolubly → It is formed from "in-" (meaning not) and "solubilis" (from Latin, meaning able to be dissolved). The word "insolubly" means in a manner that cannot be dissolved or resolved.
Think of 'not' ('in-') being able to be 'dissolved' ('solubilis') — that's why insolubly means something that cannot be dissolved.