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

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


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

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

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

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

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

Solving
-16x2 + x4 = 0

Solving for variable 'x'.

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

Factor a difference between two squares.
x2((4 + x)(-4 + x)) = 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 + 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
Solution
x = {0, -4, 4}

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