(2x+6)(x+6)=680

Solution for (2x+6)(x+6)=680 equation:

Simplifying
(2x + 6)(x + 6) = 680

Reorder the terms:
(6 + 2x)(x + 6) = 680

Reorder the terms:
(6 + 2x)(6 + x) = 680

Multiply (6 + 2x) * (6 + x)
(6(6 + x) + 2x * (6 + x)) = 680
((6 * 6 + x * 6) + 2x * (6 + x)) = 680
((36 + 6x) + 2x * (6 + x)) = 680
(36 + 6x + (6 * 2x + x * 2x)) = 680
(36 + 6x + (12x + 2x2)) = 680

Combine like terms: 6x + 12x = 18x
(36 + 18x + 2x2) = 680

Solving
36 + 18x + 2x2 = 680

Solving for variable 'x'.

Reorder the terms:
36 + -680 + 18x + 2x2 = 680 + -680

Combine like terms: 36 + -680 = -644
-644 + 18x + 2x2 = 680 + -680

Combine like terms: 680 + -680 = 0
-644 + 18x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-322 + 9x + x2) = 0

Factor a trinomial.
2((-23 + -1x)(14 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-23 + -1x)' equal to zero and attempt to solve:

Simplifying
-23 + -1x = 0

Solving
-23 + -1x = 0

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

Add '23' to each side of the equation.
-23 + 23 + -1x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -1x = 0 + 23
-1x = 0 + 23

Combine like terms: 0 + 23 = 23
-1x = 23

Divide each side by '-1'.
x = -23

Simplifying
x = -23
Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {-23, 14}