Find the real solutions of the equation by factoring: x^3-36x=16(x-6)

Question

Basic Concepts and skills

Answer 1

x³ - 36x = 16(x-6) => x(x² - 36) = 16(x-6) [notice on the left we now have the difference of two squares]

                            => x(x - 6)(x+6) = 16(x-6)

                            =>x(x - 6)(x+6) - 16(x - 6) = 0 [now we can factor x-6 from both terms]

                            => (x - 6)(x(x + 6) -16) = 0

                            => (x- 6)(x² + 6x - 16) = 0

                            => (x - 6)(x + 8)(x - 2) = 0

So now that we have our factorization, our solutions are the values of x which make this equation true. 

That is x = 6, x = -8, and x = 2