(7+2x)(6+2x)=156

Solution for (7+2x)(6+2x)=156 equation:

Simplifying
(7 + 2x)(6 + 2x) = 156

Multiply (7 + 2x) * (6 + 2x)
(7(6 + 2x) + 2x * (6 + 2x)) = 156
((6 * 7 + 2x * 7) + 2x * (6 + 2x)) = 156
((42 + 14x) + 2x * (6 + 2x)) = 156
(42 + 14x + (6 * 2x + 2x * 2x)) = 156
(42 + 14x + (12x + 4x2)) = 156

Combine like terms: 14x + 12x = 26x
(42 + 26x + 4x2) = 156

Solving
42 + 26x + 4x2 = 156

Solving for variable 'x'.

Reorder the terms:
42 + -156 + 26x + 4x2 = 156 + -156

Combine like terms: 42 + -156 = -114
-114 + 26x + 4x2 = 156 + -156

Combine like terms: 156 + -156 = 0
-114 + 26x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-57 + 13x + 2x2) = 0

Factor a trinomial.
2((-19 + -2x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-19 + -2x)' equal to zero and attempt to solve:

Simplifying
-19 + -2x = 0

Solving
-19 + -2x = 0

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

Add '19' to each side of the equation.
-19 + 19 + -2x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -2x = 0 + 19
-2x = 0 + 19

Combine like terms: 0 + 19 = 19
-2x = 19

Divide each side by '-2'.
x = -9.5

Simplifying
x = -9.5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-9.5, 3}