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 + x^{2})) = 24x
Combine like terms: 6x + -4x = 2x
x(-24 + 2x + x^{2}) = 24x
(-24 * x + 2x * x + x^{2} * x) = 24x
(-24x + 2x^{2} + x^{3}) = 24x
Solving
-24x + 2x^{2} + x^{3} = 24x
Solving for variable 'x'.
Reorder the terms:
-24x + -24x + 2x^{2} + x^{3} = 24x + -24x
Combine like terms: -24x + -24x = -48x
-48x + 2x^{2} + x^{3} = 24x + -24x
Combine like terms: 24x + -24x = 0
-48x + 2x^{2} + x^{3} = 0
Factor out the Greatest Common Factor (GCF), 'x'.
x(-48 + 2x + x^{2}) = 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}