x^3 - 6x^2 - 7x = 0
Factor out the gcf, x, first then factor the remaining trinomial. Use zero product property to find the solutions.
x^3 - 6x^2 - 7x = 0 iff
x(x^2 - 6x - 7) = 0 iff
x(x - 7)(x + 1) = 0 iff
x = 0 or x - 7 = 0 or x + 1 = 0 iff
x = 0 or x = 7 or x = -1