(x+4)*(2x+4)=112

Solution for (x+4)*(2x+4)=112 equation:

Simplifying
(x + 4)(2x + 4) = 112

Reorder the terms:
(4 + x)(2x + 4) = 112

Reorder the terms:
(4 + x)(4 + 2x) = 112

Multiply (4 + x) * (4 + 2x)
(4(4 + 2x) + x(4 + 2x)) = 112
((4 * 4 + 2x * 4) + x(4 + 2x)) = 112
((16 + 8x) + x(4 + 2x)) = 112
(16 + 8x + (4 * x + 2x * x)) = 112
(16 + 8x + (4x + 2x2)) = 112

Combine like terms: 8x + 4x = 12x
(16 + 12x + 2x2) = 112

Solving
16 + 12x + 2x2 = 112

Solving for variable 'x'.

Reorder the terms:
16 + -112 + 12x + 2x2 = 112 + -112

Combine like terms: 16 + -112 = -96
-96 + 12x + 2x2 = 112 + -112

Combine like terms: 112 + -112 = 0
-96 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + 6x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-48 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-48 + 6x + x2 = 0

Solving
-48 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 6x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 6x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 6x + x2 = 0 + 48
6x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
6x + x2 = 48

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 48 + 9

Reorder the terms:
9 + 6x + x2 = 48 + 9

Combine like terms: 48 + 9 = 57
9 + 6x + x2 = 57

Factor a perfect square on the left side:
(x + 3)(x + 3) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(x + 3) equal to 7.549834435 and -7.549834435.

Subproblem 1
x + 3 = 7.549834435

Simplifying
x + 3 = 7.549834435

Reorder the terms:
3 + x = 7.549834435

Solving
3 + x = 7.549834435

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 7.549834435 + -3

Combine like terms: 3 + -3 = 0
0 + x = 7.549834435 + -3
x = 7.549834435 + -3

Combine like terms: 7.549834435 + -3 = 4.549834435
x = 4.549834435

Simplifying
x = 4.549834435

Subproblem 2
x + 3 = -7.549834435

Simplifying
x + 3 = -7.549834435

Reorder the terms:
3 + x = -7.549834435

Solving
3 + x = -7.549834435

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -7.549834435 + -3

Combine like terms: 3 + -3 = 0
0 + x = -7.549834435 + -3
x = -7.549834435 + -3

Combine like terms: -7.549834435 + -3 = -10.549834435
x = -10.549834435

Simplifying
x = -10.549834435

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.549834435, -10.549834435}
Solution
x = {4.549834435, -10.549834435}