2x^2 - 12x - 32
= 2 (x^2 - 6x - 16)
= 2 (x^2 + 2x - 8x - 16)
= 2 [x(x+2) - 8(x+2)]
= 2 (x+2)(x-8)
you don't necessarily have to randomly search for this, remember that in a quadratic equation ax^2 + bx + c and you need to factor a polynomial, find 2 numbers that add up to b and have the product of a x c.