"I can't find a solution for this problem"
This is correct, if you are researching books or journals in search of the answer that someone else came up with (e.g. some major structural engineering problem that had to be tackled and solved when building a bridge or other structure) and finding out how they solved the problem would assist you ; or the 'answer page' at the back of a book (for problems or exercises presented for solution in the text) is missing.
If you yourself are trying to work out a solution to a problem and can't do it, then you would say:
"I can't find a solution to this problem"
Student or Learner