The usual preposition to use with solution is to, not of:
✗ The role of the government is to find the solution of this problem.
✓ The role of the government is to find the solution to this problem.
You can also use for, but this is much less common:
To find the best solutions for managing waste, all these options have to be considered.
The preposition of is used with solution mainly in technical contexts, when it refers to a liquid with another substance dissolved in it:
The containers are cleaned with a weak solution of caustic soda.