2x(2x+4)=126

Solution for 2x(2x+4)=126 equation:

Simplifying
2x(2x + 4) = 126

Reorder the terms:
2x(4 + 2x) = 126
(4 * 2x + 2x * 2x) = 126
(8x + 4x2) = 126

Solving
8x + 4x2 = 126

Solving for variable 'x'.

Reorder the terms:
-126 + 8x + 4x2 = 126 + -126

Combine like terms: 126 + -126 = 0
-126 + 8x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-63 + 4x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-63 + 4x + 2x2)' equal to zero and attempt to solve:

Simplifying
-63 + 4x + 2x2 = 0

Solving
-63 + 4x + 2x2 = 0

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

Divide each side by '2'.
-31.5 + 2x + x2 = 0

Move the constant term to the right:

Add '31.5' to each side of the equation.
-31.5 + 2x + 31.5 + x2 = 0 + 31.5

Reorder the terms:
-31.5 + 31.5 + 2x + x2 = 0 + 31.5

Combine like terms: -31.5 + 31.5 = 0.0
0.0 + 2x + x2 = 0 + 31.5
2x + x2 = 0 + 31.5

Combine like terms: 0 + 31.5 = 31.5
2x + x2 = 31.5

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 = 31.5 + 1

Reorder the terms:
1 + 2x + x2 = 31.5 + 1

Combine like terms: 31.5 + 1 = 32.5
1 + 2x + x2 = 32.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 32.5

Calculate the square root of the right side: 5.700877125

Break this problem into two subproblems by setting 
(x + 1) equal to 5.700877125 and -5.700877125.

Subproblem 1
x + 1 = 5.700877125

Simplifying
x + 1 = 5.700877125

Reorder the terms:
1 + x = 5.700877125

Solving
1 + x = 5.700877125

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 = 5.700877125 + -1

Combine like terms: 1 + -1 = 0
0 + x = 5.700877125 + -1
x = 5.700877125 + -1

Combine like terms: 5.700877125 + -1 = 4.700877125
x = 4.700877125

Simplifying
x = 4.700877125

Subproblem 2
x + 1 = -5.700877125

Simplifying
x + 1 = -5.700877125

Reorder the terms:
1 + x = -5.700877125

Solving
1 + x = -5.700877125

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 = -5.700877125 + -1

Combine like terms: 1 + -1 = 0
0 + x = -5.700877125 + -1
x = -5.700877125 + -1

Combine like terms: -5.700877125 + -1 = -6.700877125
x = -6.700877125

Simplifying
x = -6.700877125

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.700877125, -6.700877125}
Solution
x = {4.700877125, -6.700877125}