Well, do you want to solve them algebraic/symbolically or through brute force, i.e. testing all the values ?

In the first case you might use a mathematics package (a free alternative would be gap, for money you can get maple, mathematica, magma,...) and use perl to translate your problem into the language of that package

In the second case it might be better to write the search code in C and only do the parsing in perl as the search space grows fast with the number of variables

For the parsing you might use Parse::RecDescent, but if you never have anything more complicated than what you showed in the example, that would be overkill