0=x^2(x-4)(x+4)

Solution for 0=x^2(x-4)(x+4) equation:

Simplifying
0 = x2(x + -4)(x + 4)

Reorder the terms:
0 = x2(-4 + x)(x + 4)

Reorder the terms:
0 = x2(-4 + x)(4 + x)

Multiply (-4 + x) * (4 + x)
0 = x2(-4(4 + x) + x(4 + x))
0 = x2((4 * -4 + x * -4) + x(4 + x))
0 = x2((-16 + -4x) + x(4 + x))
0 = x2(-16 + -4x + (4 * x + x * x))
0 = x2(-16 + -4x + (4x + x2))

Combine like terms: -4x + 4x = 0
0 = x2(-16 + 0 + x2)
0 = x2(-16 + x2)
0 = (-16 * x2 + x2 * x2)
0 = (-16x2 + x4)

Solving
0 = -16x2 + x4

Solving for variable 'x'.
Remove the zero:
16x2 + -1x4 = -16x2 + x4 + 16x2 + -1x4

Reorder the terms:
16x2 + -1x4 = -16x2 + 16x2 + x4 + -1x4

Combine like terms: -16x2 + 16x2 = 0
16x2 + -1x4 = 0 + x4 + -1x4
16x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
16x2 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(16 + -1x2) = 0

Factor a difference between two squares.
x2((4 + x)(4 + -1x)) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

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