(x+4)(2x+2)=(3x)(20-2x)+(6x+12)

Solution for (x+4)(2x+2)=(3x)(20-2x)+(6x+12) equation:

Simplifying
(x + 4)(2x + 2) = (3x)(20 + -2x) + (6x + 12)

Reorder the terms:
(4 + x)(2x + 2) = (3x)(20 + -2x) + (6x + 12)

Reorder the terms:
(4 + x)(2 + 2x) = (3x)(20 + -2x) + (6x + 12)

Multiply (4 + x) * (2 + 2x)
(4(2 + 2x) + x(2 + 2x)) = (3x)(20 + -2x) + (6x + 12)
((2 * 4 + 2x * 4) + x(2 + 2x)) = (3x)(20 + -2x) + (6x + 12)
((8 + 8x) + x(2 + 2x)) = (3x)(20 + -2x) + (6x + 12)
(8 + 8x + (2 * x + 2x * x)) = (3x)(20 + -2x) + (6x + 12)
(8 + 8x + (2x + 2x2)) = (3x)(20 + -2x) + (6x + 12)

Combine like terms: 8x + 2x = 10x
(8 + 10x + 2x2) = (3x)(20 + -2x) + (6x + 12)

Remove parenthesis around (3x)
8 + 10x + 2x2 = 3x(20 + -2x) + (6x + 12)
8 + 10x + 2x2 = (20 * 3x + -2x * 3x) + (6x + 12)
8 + 10x + 2x2 = (60x + -6x2) + (6x + 12)

Reorder the terms:
8 + 10x + 2x2 = 60x + -6x2 + (12 + 6x)

Remove parenthesis around (12 + 6x)
8 + 10x + 2x2 = 60x + -6x2 + 12 + 6x

Reorder the terms:
8 + 10x + 2x2 = 12 + 60x + 6x + -6x2

Combine like terms: 60x + 6x = 66x
8 + 10x + 2x2 = 12 + 66x + -6x2

Solving
8 + 10x + 2x2 = 12 + 66x + -6x2

Solving for variable 'x'.

Reorder the terms:
8 + -12 + 10x + -66x + 2x2 + 6x2 = 12 + 66x + -6x2 + -12 + -66x + 6x2

Combine like terms: 8 + -12 = -4
-4 + 10x + -66x + 2x2 + 6x2 = 12 + 66x + -6x2 + -12 + -66x + 6x2

Combine like terms: 10x + -66x = -56x
-4 + -56x + 2x2 + 6x2 = 12 + 66x + -6x2 + -12 + -66x + 6x2

Combine like terms: 2x2 + 6x2 = 8x2
-4 + -56x + 8x2 = 12 + 66x + -6x2 + -12 + -66x + 6x2

Reorder the terms:
-4 + -56x + 8x2 = 12 + -12 + 66x + -66x + -6x2 + 6x2

Combine like terms: 12 + -12 = 0
-4 + -56x + 8x2 = 0 + 66x + -66x + -6x2 + 6x2
-4 + -56x + 8x2 = 66x + -66x + -6x2 + 6x2

Combine like terms: 66x + -66x = 0
-4 + -56x + 8x2 = 0 + -6x2 + 6x2
-4 + -56x + 8x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-4 + -56x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -14x + 2x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -14x + 2x2)' equal to zero and attempt to solve:

Simplifying
-1 + -14x + 2x2 = 0

Solving
-1 + -14x + 2x2 = 0

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

Divide each side by '2'.
-0.5 + -7x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -7x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -7x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -7x + x2 = 0 + 0.5
-7x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-7x + x2 = 0.5

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 0.5 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 0.5 + 12.25

Combine like terms: 0.5 + 12.25 = 12.75
12.25 + -7x + x2 = 12.75

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 12.75

Calculate the square root of the right side: 3.570714214

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.570714214 and -3.570714214.

Subproblem 1
x + -3.5 = 3.570714214

Simplifying
x + -3.5 = 3.570714214

Reorder the terms:
-3.5 + x = 3.570714214

Solving
-3.5 + x = 3.570714214

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 3.570714214 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 3.570714214 + 3.5
x = 3.570714214 + 3.5

Combine like terms: 3.570714214 + 3.5 = 7.070714214
x = 7.070714214

Simplifying
x = 7.070714214

Subproblem 2
x + -3.5 = -3.570714214

Simplifying
x + -3.5 = -3.570714214

Reorder the terms:
-3.5 + x = -3.570714214

Solving
-3.5 + x = -3.570714214

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -3.570714214 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -3.570714214 + 3.5
x = -3.570714214 + 3.5

Combine like terms: -3.570714214 + 3.5 = -0.070714214
x = -0.070714214

Simplifying
x = -0.070714214

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.070714214, -0.070714214}
Solution
x = {7.070714214, -0.070714214}