How do you find all real and complex roots?

Answer 1

In general this question is unanswerable.

However, you can consider Newton's method to make very good estimates.

Equations can be very complex in that their curves have poles and zeros where you do not expect them. Consider Riemann's Zeta function Z(z) = Sum(1/n^z, n>0). It has complex zeros on the line z=1/2, but up to this date, the distribution of the zeros is not entirely known!