Simplifying
x(x + 6)(x + -4) = 24x

Reorder the terms:
x(6 + x)(x + -4) = 24x

Reorder the terms:
x(6 + x)(-4 + x) = 24x

Multiply (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

Combine like terms: 6x + -4x = 2x
x(-24 + 2x + x2) = 24x
(-24 * x + 2x * x + x2 * x) = 24x
(-24x + 2x2 + x3) = 24x

Solving
-24x + 2x2 + x3 = 24x

Solving for variable 'x'.

Reorder the terms:
-24x + -24x + 2x2 + x3 = 24x + -24x

Combine like terms: -24x + -24x = -48x
-48x + 2x2 + x3 = 24x + -24x

Combine like terms: 24x + -24x = 0
-48x + 2x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-48 + 2x + x2) = 0

Factor a trinomial.
x((-8 + -1x)(6 + -1x)) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
Subproblem 2
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, -8, 6}