Find the zeroes of this polynomial function

f(x)=x^3+x^2-6x
Please explain step by step?

Factor out an x:
f(x) = x(x^2 + x - 6)

What multiplies to -6*1 and adds to 1? -2 and 3 work:
f(x) = x(x - 2)(x + 3)

Set it equal to 0:
x(x - 2)(x + 3) = 0

so either x = 0, x - 2 = 0, or x + 3 = 0, which means that x = 0, 2 or -3.