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The phrase "are hard to solve" is correct and usable in written English.
You can use it when discussing problems, puzzles, or challenges that require significant effort or skill to find a solution.
Example: "Mathematical equations can sometimes be very complex, and certain problems are hard to solve without advanced knowledge."
Alternatives: "are difficult to resolve" or "are challenging to tackle".
Exact(23)
Some problems are hard to solve.
These methods require complex initialization procedures and they are hard to solve.
The practical control problems are hard to solve using analytical approaches.
It is just that the problem general methods are hard to solve.
These clues are easy to spot, even if they are hard to solve, because the word Spooner or spoonerism will alert you to what is required.
Routing problems constitute an important class of problems because they are hard to solve and have a wide variety of real-world applications.
Similar(37)
(Murders are harder to solve).
Our numerical results indicate that the ring models are harder to solve with CPLEX than the tree and star ones.
For too long, overly ambitious global climate talks have focused on the aspects of global warming that are hardest to solve.
Experts said it might stop people using weak passwords but could lead to other loopholes that are harder to solve.
If there ever was a problem that's hard to solve, it's climate change.
More suggestions(16)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com