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

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

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

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

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

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

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

Reorder the terms:
-4 + 2x + 2x2 = (6 + x)(x + 4)

Reorder the terms:
-4 + 2x + 2x2 = (6 + x)(4 + x)

Multiply (6 + x) * (4 + x)
-4 + 2x + 2x2 = (6(4 + x) + x(4 + x))
-4 + 2x + 2x2 = ((4 * 6 + x * 6) + x(4 + x))
-4 + 2x + 2x2 = ((24 + 6x) + x(4 + x))
-4 + 2x + 2x2 = (24 + 6x + (4 * x + x * x))
-4 + 2x + 2x2 = (24 + 6x + (4x + x2))

Combine like terms: 6x + 4x = 10x
-4 + 2x + 2x2 = (24 + 10x + x2)

Solving
-4 + 2x + 2x2 = 24 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
-4 + -24 + 2x + -10x + 2x2 + -1x2 = 24 + 10x + x2 + -24 + -10x + -1x2

Combine like terms: -4 + -24 = -28
-28 + 2x + -10x + 2x2 + -1x2 = 24 + 10x + x2 + -24 + -10x + -1x2

Combine like terms: 2x + -10x = -8x
-28 + -8x + 2x2 + -1x2 = 24 + 10x + x2 + -24 + -10x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-28 + -8x + 1x2 = 24 + 10x + x2 + -24 + -10x + -1x2

Reorder the terms:
-28 + -8x + 1x2 = 24 + -24 + 10x + -10x + x2 + -1x2

Combine like terms: 24 + -24 = 0
-28 + -8x + 1x2 = 0 + 10x + -10x + x2 + -1x2
-28 + -8x + 1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-28 + -8x + 1x2 = 0 + x2 + -1x2
-28 + -8x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-28 + -8x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -8x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + -8x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -8x + x2 = 0 + 28
-8x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
-8x + x2 = 28

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 28 + 16

Reorder the terms:
16 + -8x + x2 = 28 + 16

Combine like terms: 28 + 16 = 44
16 + -8x + x2 = 44

Factor a perfect square on the left side:
(x + -4)(x + -4) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(x + -4) equal to 6.633249581 and -6.633249581.

Subproblem 1
x + -4 = 6.633249581

Simplifying
x + -4 = 6.633249581

Reorder the terms:
-4 + x = 6.633249581

Solving
-4 + x = 6.633249581

Solving for variable 'x'.

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 = 6.633249581 + 4

Combine like terms: -4 + 4 = 0
0 + x = 6.633249581 + 4
x = 6.633249581 + 4

Combine like terms: 6.633249581 + 4 = 10.633249581
x = 10.633249581

Simplifying
x = 10.633249581

Subproblem 2
x + -4 = -6.633249581

Simplifying
x + -4 = -6.633249581

Reorder the terms:
-4 + x = -6.633249581

Solving
-4 + x = -6.633249581

Solving for variable 'x'.

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 = -6.633249581 + 4

Combine like terms: -4 + 4 = 0
0 + x = -6.633249581 + 4
x = -6.633249581 + 4

Combine like terms: -6.633249581 + 4 = -2.633249581
x = -2.633249581

Simplifying
x = -2.633249581

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.633249581, -2.633249581}