Question

How do you simplify an algebraic equation with more than one variable?

Answer 1

a nonlinear equation can sometimes be simplified by first rewriting it as Something=0, then trying to factor the left hand side...
... for instance, \[x y^2=x\] will lead to \[x y^2 - x = 0\] then \[x(y-1)(y+1)=0\] so the solutions are x=0, y=1, y=-1.
Not sure whether this helps - you may want to provide a more specific example of a type of equation you have in mind...