Not all problems you can write down have some nuce simple algebraic solution. In fact, almost all problems you can write down do not have one. It is the rare and relatively simple problems that have a solution. We get spoiled, because homework assignments always have a solution. After all, why would your teacher assign something that has no solution, unless they were being particularly unpleasant?
And of course, there ARE problems that in fact, do have a solution, but a solver cannot find it. Sadly, they are difficult, but there is often no magic wand that can be waved, beyond doing good mathematics. Sometimes a transformation exists that the solver did not find. These problems tend to be rather rare though.
Just wanting something to happen is not sufficient though, unless of course, you do have a working magic wand. Mine broke the other day though, and spare parts for magic mathematical wands are hard to come by.
