(x+6)(2x+6)=756

Solution for (x+6)(2x+6)=756 equation:

Simplifying
(x + 6)(2x + 6) = 756

Reorder the terms:
(6 + x)(2x + 6) = 756

Reorder the terms:
(6 + x)(6 + 2x) = 756

Multiply (6 + x) * (6 + 2x)
(6(6 + 2x) + x(6 + 2x)) = 756
((6 * 6 + 2x * 6) + x(6 + 2x)) = 756
((36 + 12x) + x(6 + 2x)) = 756
(36 + 12x + (6 * x + 2x * x)) = 756
(36 + 12x + (6x + 2x2)) = 756

Combine like terms: 12x + 6x = 18x
(36 + 18x + 2x2) = 756

Solving
36 + 18x + 2x2 = 756

Solving for variable 'x'.

Reorder the terms:
36 + -756 + 18x + 2x2 = 756 + -756

Combine like terms: 36 + -756 = -720
-720 + 18x + 2x2 = 756 + -756

Combine like terms: 756 + -756 = 0
-720 + 18x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-360 + 9x + x2) = 0

Factor a trinomial.
2((-24 + -1x)(15 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-24 + -1x)' equal to zero and attempt to solve:

Simplifying
-24 + -1x = 0

Solving
-24 + -1x = 0

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

Add '24' to each side of the equation.
-24 + 24 + -1x = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1x = 0 + 24
-1x = 0 + 24

Combine like terms: 0 + 24 = 24
-1x = 24

Divide each side by '-1'.
x = -24

Simplifying
x = -24
Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {-24, 15}