(2x+8)(6x+12)=180

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Solution for (2x+8)(6x+12)=180 equation: 


Simplifying
(2x + 8)(6x + 12) = 180

Reorder the terms:
(8 + 2x)(6x + 12) = 180

Reorder the terms:
(8 + 2x)(12 + 6x) = 180

Multiply (8 + 2x) * (12 + 6x)
(8(12 + 6x) + 2x * (12 + 6x)) = 180
((12 * 8 + 6x * 8) + 2x * (12 + 6x)) = 180
((96 + 48x) + 2x * (12 + 6x)) = 180
(96 + 48x + (12 * 2x + 6x * 2x)) = 180
(96 + 48x + (24x + 12x2)) = 180

Combine like terms: 48x + 24x = 72x
(96 + 72x + 12x2) = 180

Solving
96 + 72x + 12x2 = 180

Solving for variable 'x'.

Reorder the terms:
96 + -180 + 72x + 12x2 = 180 + -180

Combine like terms: 96 + -180 = -84
-84 + 72x + 12x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-84 + 72x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-7 + 6x + x2) = 0

Factor a trinomial.
12((-7 + -1x)(1 + -1x)) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-7, 1}

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