What are the zeros of the function? f(x)=5x3+10x2−15x?

First thing to do here is to factor out the common 5x.  When you do that you end up with this: .  It's easy enough now to factor the second degree polynomial inside the parenthesis. The 2 numbers that add up to be 2 and multiply to be -3 are x = 1 and x = -3.  But we also have to consider the fact that 5x = 0 and x = 0.  This is a third degree polynomial, after all, so we need to find 3 solutions.  Here they all are:  x = -3, 0, 1