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

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

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

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

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

Reorder the terms for easier multiplication:
x2 = (x(-4 + x)(4 + x))

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

Combine like terms: -4x + 4x = 0
x2 = (x(-16 + 0 + x2))
x2 = (x(-16 + x2))
x2 = ((-16 * x + x2 * x))
x2 = ((-16x + x3))
x2 = (-16x + x3)

Remove parenthesis around (-16x + x3)
x2 = -16x + x3

Solving
x2 = -16x + x3

Solving for variable 'x'.

Reorder the terms:
16x + x2 + -1x3 = -16x + x3 + 16x + -1x3

Reorder the terms:
16x + x2 + -1x3 = -16x + 16x + x3 + -1x3

Combine like terms: -16x + 16x = 0
16x + x2 + -1x3 = 0 + x3 + -1x3
16x + x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
16x + x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(16 + x + -1x2) = 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 '(16 + x + -1x2)' equal to zero and attempt to solve:

Simplifying
16 + x + -1x2 = 0

Solving
16 + x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-16 + -1x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -1x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -1x + x2 = 0 + 16

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

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

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 16 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 16 + 0.25

Combine like terms: 16 + 0.25 = 16.25
0.25 + -1x + x2 = 16.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.031128874 and -4.031128874.

Subproblem 1
x + 0.5 = 4.031128874

Simplifying
x + 0.5 = 4.031128874

Reorder the terms:
0.5 + x = 4.031128874

Solving
0.5 + x = 4.031128874

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 4.031128874 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4.031128874 + -0.5
x = 4.031128874 + -0.5

Combine like terms: 4.031128874 + -0.5 = 3.531128874
x = 3.531128874

Simplifying
x = 3.531128874

Subproblem 2
x + 0.5 = -4.031128874

Simplifying
x + 0.5 = -4.031128874

Reorder the terms:
0.5 + x = -4.031128874

Solving
0.5 + x = -4.031128874

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -4.031128874 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4.031128874 + -0.5
x = -4.031128874 + -0.5

Combine like terms: -4.031128874 + -0.5 = -4.531128874
x = -4.531128874

Simplifying
x = -4.531128874

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.531128874, -4.531128874}
Solution
x = {0, 3.531128874, -4.531128874}