(2x+6)x=156

Solution for (2x+6)x=156 equation:

Simplifying
(2x + 6) * x = 156

Reorder the terms:
(6 + 2x) * x = 156

Reorder the terms for easier multiplication:
x(6 + 2x) = 156
(6 * x + 2x * x) = 156
(6x + 2x2) = 156

Solving
6x + 2x2 = 156

Solving for variable 'x'.

Reorder the terms:
-156 + 6x + 2x2 = 156 + -156

Combine like terms: 156 + -156 = 0
-156 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-78 + 3x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-78 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-78 + 3x + x2 = 0

Solving
-78 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '78' to each side of the equation.
-78 + 3x + 78 + x2 = 0 + 78

Reorder the terms:
-78 + 78 + 3x + x2 = 0 + 78

Combine like terms: -78 + 78 = 0
0 + 3x + x2 = 0 + 78
3x + x2 = 0 + 78

Combine like terms: 0 + 78 = 78
3x + x2 = 78

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 78 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 78 + 2.25

Combine like terms: 78 + 2.25 = 80.25
2.25 + 3x + x2 = 80.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 80.25

Calculate the square root of the right side: 8.958236434

Break this problem into two subproblems by setting 
(x + 1.5) equal to 8.958236434 and -8.958236434.

Subproblem 1
x + 1.5 = 8.958236434

Simplifying
x + 1.5 = 8.958236434

Reorder the terms:
1.5 + x = 8.958236434

Solving
1.5 + x = 8.958236434

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 8.958236434 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 8.958236434 + -1.5
x = 8.958236434 + -1.5

Combine like terms: 8.958236434 + -1.5 = 7.458236434
x = 7.458236434

Simplifying
x = 7.458236434

Subproblem 2
x + 1.5 = -8.958236434

Simplifying
x + 1.5 = -8.958236434

Reorder the terms:
1.5 + x = -8.958236434

Solving
1.5 + x = -8.958236434

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -8.958236434 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -8.958236434 + -1.5
x = -8.958236434 + -1.5

Combine like terms: -8.958236434 + -1.5 = -10.458236434
x = -10.458236434

Simplifying
x = -10.458236434

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.458236434, -10.458236434}
Solution
x = {7.458236434, -10.458236434}