This is the 17140th most frequent Turkish word.
çözülmeyecek
"Çözülmeyecek" means "that will not be solved" or "unsolvable."
Here, 'çözülmeyecek' is used adjectivally to describe 'bir yanı', meaning 'an aspect', indicating that it's something that cannot be solved.
Bu sorunun çözülmeyecek bir yanı yok.
There is no aspect of this problem that cannot be solved.
In this sentence, 'çözülmeyecek' modifies 'bir düğüm', meaning 'a knot', and it conveys the sense of a knot that is seemingly impossible to untangle or undo.
Çözülmeyecek bir düğümle uğraştığımızı düşündüm.
I thought we were dealing with a knot that cannot be untied.
Here, 'çözülmeyecek' is used in a predicative construction, suggesting the fate or future resolution status of 'sorun', meaning 'problem', as something not expected to resolve.