As a method it is used Newton´s tangent method generalised for more variables. Method is iterative and converges quickly for large set of functions. Principle of the method implies that it will find soultion quickly if starting points are not far away from solution and if functions are continuosly differentiable with non-zero derivations. (For linear equations it will always find solution in first steps, if exactly one exists.)
If program will not find solution and you believe it exists, you can start with different starting points.
If program is close to solution but not precise enought, you can set higher number of itarations, but it can cause that more time is needed for computation.