5(x+6)(x+6)+21=126

Solution for 5(x+6)(x+6)+21=126 equation:

Simplifying
5(x + 6)(x + 6) + 21 = 126

Reorder the terms:
5(6 + x)(x + 6) + 21 = 126

Reorder the terms:
5(6 + x)(6 + x) + 21 = 126

Multiply (6 + x) * (6 + x)
5(6(6 + x) + x(6 + x)) + 21 = 126
5((6 * 6 + x * 6) + x(6 + x)) + 21 = 126
5((36 + 6x) + x(6 + x)) + 21 = 126
5(36 + 6x + (6 * x + x * x)) + 21 = 126
5(36 + 6x + (6x + x2)) + 21 = 126

Combine like terms: 6x + 6x = 12x
5(36 + 12x + x2) + 21 = 126
(36 * 5 + 12x * 5 + x2 * 5) + 21 = 126
(180 + 60x + 5x2) + 21 = 126

Reorder the terms:
180 + 21 + 60x + 5x2 = 126

Combine like terms: 180 + 21 = 201
201 + 60x + 5x2 = 126

Solving
201 + 60x + 5x2 = 126

Solving for variable 'x'.

Reorder the terms:
201 + -126 + 60x + 5x2 = 126 + -126

Combine like terms: 201 + -126 = 75
75 + 60x + 5x2 = 126 + -126

Combine like terms: 126 + -126 = 0
75 + 60x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(15 + 12x + x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(15 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
15 + 12x + x2 = 0

Solving
15 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 12x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + 12x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 12x + x2 = 0 + -15
12x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
12x + x2 = -15

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -15 + 36

Reorder the terms:
36 + 12x + x2 = -15 + 36

Combine like terms: -15 + 36 = 21
36 + 12x + x2 = 21

Factor a perfect square on the left side:
(x + 6)(x + 6) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + 6) equal to 4.582575695 and -4.582575695.

Subproblem 1
x + 6 = 4.582575695

Simplifying
x + 6 = 4.582575695

Reorder the terms:
6 + x = 4.582575695

Solving
6 + x = 4.582575695

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 4.582575695 + -6

Combine like terms: 6 + -6 = 0
0 + x = 4.582575695 + -6
x = 4.582575695 + -6

Combine like terms: 4.582575695 + -6 = -1.417424305
x = -1.417424305

Simplifying
x = -1.417424305

Subproblem 2
x + 6 = -4.582575695

Simplifying
x + 6 = -4.582575695

Reorder the terms:
6 + x = -4.582575695

Solving
6 + x = -4.582575695

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -4.582575695 + -6

Combine like terms: 6 + -6 = 0
0 + x = -4.582575695 + -6
x = -4.582575695 + -6

Combine like terms: -4.582575695 + -6 = -10.582575695
x = -10.582575695

Simplifying
x = -10.582575695

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.417424305, -10.582575695}
Solution
x = {-1.417424305, -10.582575695}