Question

Did I do this problem the correct way if so is there a shorter way to explain this?
x(x + 6)(x + -4) = 24x
x(6 + x)(x + -4) = 24x
x(6 + x)(-4 + x) = 24x
(6 + x) * (-4 + x
x(6(-4 + x) + x(-4 + x)) = 24x
x((-4 * 6 + x * 6) + x(-4 + x)) = 24x
x((-24 + 6x) + x(-4 + x)) = 24x
x(-24 + 6x + (-4 * x + x * x)) = 24x
x(-24 + 6x + (-4x + x2)) = 24x
6x + -4x = 2x
x(-24 + 2x + x2) = 24x
(-24 * x + 2x * x + x2 * x) = 24x
(-24x + 2x2 + x3) = 24x
-24x + 2x2 + x3 = 24x
-24x + -24x + 2x2 + x3 = 24x + -24x
-24x + -24x = -48x
-48x + 2x2 + x3 = 24x + -24x
24x + -24x = 0
-48x + 2x2 + x3 = 0
x(-48 + 2x + x2) = 0
x((-8 + -1x)(6 + -1x)) = 0
x = 0
-8 + 8 + -1x = 0 + 8
0 + -1x = 0 + 8
-1x = 0 + 8
-1x = 8
x = -8
x = {0, -8, 6}

Answer 1

First of all, x=0 is clearly a solution.
For other solutions, divide both sides by x to get the quadratic
(x+6)(x-4) = 24
x^2 +2x -24 = 24
x^2 +2x -48 = 0
(x+8)(x-6) = 0
x = -8 or 6

Your answer is correct but you got there the hard way.