na-adjective, noun which may take the genitive case particle 'no'
unsolvable; insoluble; unresolvable
Describes a problem, puzzle, or situation that cannot be solved or resolved. Often used in formal or technical contexts.
この問題は解決不能だ。
This problem is unsolvable.
解決不能な謎に挑む。
Take on an insoluble mystery.
Compound of 解決 (solution) and 不能 (impossible). The exact historical derivation is uncertain, but the meaning is transparent from its components.