(x+6)*(x+2)=(2x-2)*(x+4)

Solution for (x+6)*(x+2)=(2x-2)*(x+4) equation:

Simplifying
(x + 6)(x + 2) = (2x + -2)(x + 4)

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

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

Multiply (6 + x) * (2 + x)
(6(2 + x) + x(2 + x)) = (2x + -2)(x + 4)
((2 * 6 + x * 6) + x(2 + x)) = (2x + -2)(x + 4)
((12 + 6x) + x(2 + x)) = (2x + -2)(x + 4)
(12 + 6x + (2 * x + x * x)) = (2x + -2)(x + 4)
(12 + 6x + (2x + x2)) = (2x + -2)(x + 4)

Combine like terms: 6x + 2x = 8x
(12 + 8x + x2) = (2x + -2)(x + 4)

Reorder the terms:
12 + 8x + x2 = (-2 + 2x)(x + 4)

Reorder the terms:
12 + 8x + x2 = (-2 + 2x)(4 + x)

Multiply (-2 + 2x) * (4 + x)
12 + 8x + x2 = (-2(4 + x) + 2x * (4 + x))
12 + 8x + x2 = ((4 * -2 + x * -2) + 2x * (4 + x))
12 + 8x + x2 = ((-8 + -2x) + 2x * (4 + x))
12 + 8x + x2 = (-8 + -2x + (4 * 2x + x * 2x))
12 + 8x + x2 = (-8 + -2x + (8x + 2x2))

Combine like terms: -2x + 8x = 6x
12 + 8x + x2 = (-8 + 6x + 2x2)

Solving
12 + 8x + x2 = -8 + 6x + 2x2

Solving for variable 'x'.

Reorder the terms:
12 + 8 + 8x + -6x + x2 + -2x2 = -8 + 6x + 2x2 + 8 + -6x + -2x2

Combine like terms: 12 + 8 = 20
20 + 8x + -6x + x2 + -2x2 = -8 + 6x + 2x2 + 8 + -6x + -2x2

Combine like terms: 8x + -6x = 2x
20 + 2x + x2 + -2x2 = -8 + 6x + 2x2 + 8 + -6x + -2x2

Combine like terms: x2 + -2x2 = -1x2
20 + 2x + -1x2 = -8 + 6x + 2x2 + 8 + -6x + -2x2

Reorder the terms:
20 + 2x + -1x2 = -8 + 8 + 6x + -6x + 2x2 + -2x2

Combine like terms: -8 + 8 = 0
20 + 2x + -1x2 = 0 + 6x + -6x + 2x2 + -2x2
20 + 2x + -1x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
20 + 2x + -1x2 = 0 + 2x2 + -2x2
20 + 2x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
20 + 2x + -1x2 = 0

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

Divide each side by '-1'.
-20 + -2x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -2x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -2x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -2x + x2 = 0 + 20
-2x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-2x + x2 = 20

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 20 + 1

Reorder the terms:
1 + -2x + x2 = 20 + 1

Combine like terms: 20 + 1 = 21
1 + -2x + x2 = 21

Factor a perfect square on the left side:
(x + -1)(x + -1) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + -1) equal to 4.582575695 and -4.582575695.

Subproblem 1
x + -1 = 4.582575695

Simplifying
x + -1 = 4.582575695

Reorder the terms:
-1 + x = 4.582575695

Solving
-1 + x = 4.582575695

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 4.582575695 + 1

Combine like terms: -1 + 1 = 0
0 + x = 4.582575695 + 1
x = 4.582575695 + 1

Combine like terms: 4.582575695 + 1 = 5.582575695
x = 5.582575695

Simplifying
x = 5.582575695

Subproblem 2
x + -1 = -4.582575695

Simplifying
x + -1 = -4.582575695

Reorder the terms:
-1 + x = -4.582575695

Solving
-1 + x = -4.582575695

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -4.582575695 + 1

Combine like terms: -1 + 1 = 0
0 + x = -4.582575695 + 1
x = -4.582575695 + 1

Combine like terms: -4.582575695 + 1 = -3.582575695
x = -3.582575695

Simplifying
x = -3.582575695

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.582575695, -3.582575695}