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

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

Simplifying
x2 = 2(x + 2)(x + -4) * 4

Reorder the terms:
x2 = 2(2 + x)(x + -4) * 4

Reorder the terms:
x2 = 2(2 + x)(-4 + x) * 4

Reorder the terms for easier multiplication:
x2 = 2 * 4(2 + x)(-4 + x)

Multiply 2 * 4
x2 = 8(2 + x)(-4 + x)

Multiply (2 + x) * (-4 + x)
x2 = 8(2(-4 + x) + x(-4 + x))
x2 = 8((-4 * 2 + x * 2) + x(-4 + x))
x2 = 8((-8 + 2x) + x(-4 + x))
x2 = 8(-8 + 2x + (-4 * x + x * x))
x2 = 8(-8 + 2x + (-4x + x2))

Combine like terms: 2x + -4x = -2x
x2 = 8(-8 + -2x + x2)
x2 = (-8 * 8 + -2x * 8 + x2 * 8)
x2 = (-64 + -16x + 8x2)

Solving
x2 = -64 + -16x + 8x2

Solving for variable 'x'.

Reorder the terms:
64 + 16x + x2 + -8x2 = -64 + -16x + 8x2 + 64 + 16x + -8x2

Combine like terms: x2 + -8x2 = -7x2
64 + 16x + -7x2 = -64 + -16x + 8x2 + 64 + 16x + -8x2

Reorder the terms:
64 + 16x + -7x2 = -64 + 64 + -16x + 16x + 8x2 + -8x2

Combine like terms: -64 + 64 = 0
64 + 16x + -7x2 = 0 + -16x + 16x + 8x2 + -8x2
64 + 16x + -7x2 = -16x + 16x + 8x2 + -8x2

Combine like terms: -16x + 16x = 0
64 + 16x + -7x2 = 0 + 8x2 + -8x2
64 + 16x + -7x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
64 + 16x + -7x2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-9.142857143 + -2.285714286x + x2 = 0

Move the constant term to the right:

Add '9.142857143' to each side of the equation.
-9.142857143 + -2.285714286x + 9.142857143 + x2 = 0 + 9.142857143

Reorder the terms:
-9.142857143 + 9.142857143 + -2.285714286x + x2 = 0 + 9.142857143

Combine like terms: -9.142857143 + 9.142857143 = 0.000000000
0.000000000 + -2.285714286x + x2 = 0 + 9.142857143
-2.285714286x + x2 = 0 + 9.142857143

Combine like terms: 0 + 9.142857143 = 9.142857143
-2.285714286x + x2 = 9.142857143

The x term is -2.285714286x.  Take half its coefficient (-1.142857143).
Square it (1.306122449) and add it to both sides.

Add '1.306122449' to each side of the equation.
-2.285714286x + 1.306122449 + x2 = 9.142857143 + 1.306122449

Reorder the terms:
1.306122449 + -2.285714286x + x2 = 9.142857143 + 1.306122449

Combine like terms: 9.142857143 + 1.306122449 = 10.448979592
1.306122449 + -2.285714286x + x2 = 10.448979592

Factor a perfect square on the left side:
(x + -1.142857143)(x + -1.142857143) = 10.448979592

Calculate the square root of the right side: 3.232488143

Break this problem into two subproblems by setting 
(x + -1.142857143) equal to 3.232488143 and -3.232488143.

Subproblem 1
x + -1.142857143 = 3.232488143

Simplifying
x + -1.142857143 = 3.232488143

Reorder the terms:
-1.142857143 + x = 3.232488143

Solving
-1.142857143 + x = 3.232488143

Solving for variable 'x'.

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

Add '1.142857143' to each side of the equation.
-1.142857143 + 1.142857143 + x = 3.232488143 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + x = 3.232488143 + 1.142857143
x = 3.232488143 + 1.142857143

Combine like terms: 3.232488143 + 1.142857143 = 4.375345286
x = 4.375345286

Simplifying
x = 4.375345286

Subproblem 2
x + -1.142857143 = -3.232488143

Simplifying
x + -1.142857143 = -3.232488143

Reorder the terms:
-1.142857143 + x = -3.232488143

Solving
-1.142857143 + x = -3.232488143

Solving for variable 'x'.

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

Add '1.142857143' to each side of the equation.
-1.142857143 + 1.142857143 + x = -3.232488143 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + x = -3.232488143 + 1.142857143
x = -3.232488143 + 1.142857143

Combine like terms: -3.232488143 + 1.142857143 = -2.089631
x = -2.089631

Simplifying
x = -2.089631

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.375345286, -2.089631}