3(x+6)(x+6)+25=61

Solution for 3(x+6)(x+6)+25=61 equation:

Simplifying
3(x + 6)(x + 6) + 25 = 61

Reorder the terms:
3(6 + x)(x + 6) + 25 = 61

Reorder the terms:
3(6 + x)(6 + x) + 25 = 61

Multiply (6 + x) * (6 + x)
3(6(6 + x) + x(6 + x)) + 25 = 61
3((6 * 6 + x * 6) + x(6 + x)) + 25 = 61
3((36 + 6x) + x(6 + x)) + 25 = 61
3(36 + 6x + (6 * x + x * x)) + 25 = 61
3(36 + 6x + (6x + x2)) + 25 = 61

Combine like terms: 6x + 6x = 12x
3(36 + 12x + x2) + 25 = 61
(36 * 3 + 12x * 3 + x2 * 3) + 25 = 61
(108 + 36x + 3x2) + 25 = 61

Reorder the terms:
108 + 25 + 36x + 3x2 = 61

Combine like terms: 108 + 25 = 133
133 + 36x + 3x2 = 61

Solving
133 + 36x + 3x2 = 61

Solving for variable 'x'.

Reorder the terms:
133 + -61 + 36x + 3x2 = 61 + -61

Combine like terms: 133 + -61 = 72
72 + 36x + 3x2 = 61 + -61

Combine like terms: 61 + -61 = 0
72 + 36x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + 12x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(24 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
24 + 12x + x2 = 0

Solving
24 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + 12x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + 12x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + 12x + x2 = 0 + -24
12x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
12x + x2 = -24

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 = -24 + 36

Reorder the terms:
36 + 12x + x2 = -24 + 36

Combine like terms: -24 + 36 = 12
36 + 12x + x2 = 12

Factor a perfect square on the left side:
(x + 6)(x + 6) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + 6) equal to 3.464101615 and -3.464101615.

Subproblem 1
x + 6 = 3.464101615

Simplifying
x + 6 = 3.464101615

Reorder the terms:
6 + x = 3.464101615

Solving
6 + x = 3.464101615

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 = 3.464101615 + -6

Combine like terms: 6 + -6 = 0
0 + x = 3.464101615 + -6
x = 3.464101615 + -6

Combine like terms: 3.464101615 + -6 = -2.535898385
x = -2.535898385

Simplifying
x = -2.535898385

Subproblem 2
x + 6 = -3.464101615

Simplifying
x + 6 = -3.464101615

Reorder the terms:
6 + x = -3.464101615

Solving
6 + x = -3.464101615

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 = -3.464101615 + -6

Combine like terms: 6 + -6 = 0
0 + x = -3.464101615 + -6
x = -3.464101615 + -6

Combine like terms: -3.464101615 + -6 = -9.464101615
x = -9.464101615

Simplifying
x = -9.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.535898385, -9.464101615}
Solution
x = {-2.535898385, -9.464101615}