(2x+4)(x+4)=124

Solution for (2x+4)(x+4)=124 equation:

Simplifying
(2x + 4)(x + 4) = 124

Reorder the terms:
(4 + 2x)(x + 4) = 124

Reorder the terms:
(4 + 2x)(4 + x) = 124

Multiply (4 + 2x) * (4 + x)
(4(4 + x) + 2x * (4 + x)) = 124
((4 * 4 + x * 4) + 2x * (4 + x)) = 124
((16 + 4x) + 2x * (4 + x)) = 124
(16 + 4x + (4 * 2x + x * 2x)) = 124
(16 + 4x + (8x + 2x2)) = 124

Combine like terms: 4x + 8x = 12x
(16 + 12x + 2x2) = 124

Solving
16 + 12x + 2x2 = 124

Solving for variable 'x'.

Reorder the terms:
16 + -124 + 12x + 2x2 = 124 + -124

Combine like terms: 16 + -124 = -108
-108 + 12x + 2x2 = 124 + -124

Combine like terms: 124 + -124 = 0
-108 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + 6x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-54 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-54 + 6x + x2 = 0

Solving
-54 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + 6x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + 6x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + 6x + x2 = 0 + 54
6x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
6x + x2 = 54

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 = 54 + 9

Reorder the terms:
9 + 6x + x2 = 54 + 9

Combine like terms: 54 + 9 = 63
9 + 6x + x2 = 63

Factor a perfect square on the left side:
(x + 3)(x + 3) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(x + 3) equal to 7.937253933 and -7.937253933.

Subproblem 1
x + 3 = 7.937253933

Simplifying
x + 3 = 7.937253933

Reorder the terms:
3 + x = 7.937253933

Solving
3 + x = 7.937253933

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 = 7.937253933 + -3

Combine like terms: 3 + -3 = 0
0 + x = 7.937253933 + -3
x = 7.937253933 + -3

Combine like terms: 7.937253933 + -3 = 4.937253933
x = 4.937253933

Simplifying
x = 4.937253933

Subproblem 2
x + 3 = -7.937253933

Simplifying
x + 3 = -7.937253933

Reorder the terms:
3 + x = -7.937253933

Solving
3 + x = -7.937253933

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 = -7.937253933 + -3

Combine like terms: 3 + -3 = 0
0 + x = -7.937253933 + -3
x = -7.937253933 + -3

Combine like terms: -7.937253933 + -3 = -10.937253933
x = -10.937253933

Simplifying
x = -10.937253933

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.937253933, -10.937253933}
Solution
x = {4.937253933, -10.937253933}