(x-8)x(x+4)=0

Solution for (x-8)x(x+4)=0 equation:

Simplifying
(x + -8) * x(x + 4) = 0

Reorder the terms:
(-8 + x) * x(x + 4) = 0

Reorder the terms:
(-8 + x) * x(4 + x) = 0

Reorder the terms for easier multiplication:
x(-8 + x)(4 + x) = 0

Multiply (-8 + x) * (4 + x)
x(-8(4 + x) + x(4 + x)) = 0
x((4 * -8 + x * -8) + x(4 + x)) = 0
x((-32 + -8x) + x(4 + x)) = 0
x(-32 + -8x + (4 * x + x * x)) = 0
x(-32 + -8x + (4x + x2)) = 0

Combine like terms: -8x + 4x = -4x
x(-32 + -4x + x2) = 0
(-32 * x + -4x * x + x2 * x) = 0
(-32x + -4x2 + x3) = 0

Solving
-32x + -4x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-32 + -4x + x2) = 0

Factor a trinomial.
x((-4 + -1x)(8 + -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 '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 3
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
Solution
x = {0, -4, 8}