x(x+x+12)=92

Solution for x(x+x+12)=92 equation:

Simplifying
x(x + x + 12) = 92

Reorder the terms:
x(12 + x + x) = 92

Combine like terms: x + x = 2x
x(12 + 2x) = 92
(12 * x + 2x * x) = 92
(12x + 2x2) = 92

Solving
12x + 2x2 = 92

Solving for variable 'x'.

Reorder the terms:
-92 + 12x + 2x2 = 92 + -92

Combine like terms: 92 + -92 = 0
-92 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-46 + 6x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-46 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-46 + 6x + x2 = 0

Solving
-46 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '46' to each side of the equation.
-46 + 6x + 46 + x2 = 0 + 46

Reorder the terms:
-46 + 46 + 6x + x2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + 6x + x2 = 0 + 46
6x + x2 = 0 + 46

Combine like terms: 0 + 46 = 46
6x + x2 = 46

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 = 46 + 9

Reorder the terms:
9 + 6x + x2 = 46 + 9

Combine like terms: 46 + 9 = 55
9 + 6x + x2 = 55

Factor a perfect square on the left side:
(x + 3)(x + 3) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(x + 3) equal to 7.416198487 and -7.416198487.

Subproblem 1
x + 3 = 7.416198487

Simplifying
x + 3 = 7.416198487

Reorder the terms:
3 + x = 7.416198487

Solving
3 + x = 7.416198487

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 = 7.416198487 + -3

Combine like terms: 3 + -3 = 0
0 + x = 7.416198487 + -3
x = 7.416198487 + -3

Combine like terms: 7.416198487 + -3 = 4.416198487
x = 4.416198487

Simplifying
x = 4.416198487

Subproblem 2
x + 3 = -7.416198487

Simplifying
x + 3 = -7.416198487

Reorder the terms:
3 + x = -7.416198487

Solving
3 + x = -7.416198487

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 = -7.416198487 + -3

Combine like terms: 3 + -3 = 0
0 + x = -7.416198487 + -3
x = -7.416198487 + -3

Combine like terms: -7.416198487 + -3 = -10.416198487
x = -10.416198487

Simplifying
x = -10.416198487

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.416198487, -10.416198487}
Solution
x = {4.416198487, -10.416198487}