(9+2x)(12+2x)=180

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Solution for (9+2x)(12+2x)=180 equation: 


Simplifying
(9 + 2x)(12 + 2x) = 180

Multiply (9 + 2x) * (12 + 2x)
(9(12 + 2x) + 2x * (12 + 2x)) = 180
((12 * 9 + 2x * 9) + 2x * (12 + 2x)) = 180
((108 + 18x) + 2x * (12 + 2x)) = 180
(108 + 18x + (12 * 2x + 2x * 2x)) = 180
(108 + 18x + (24x + 4x2)) = 180

Combine like terms: 18x + 24x = 42x
(108 + 42x + 4x2) = 180

Solving
108 + 42x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
108 + -180 + 42x + 4x2 = 180 + -180

Combine like terms: 108 + -180 = -72
-72 + 42x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-72 + 42x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + 21x + 2x2) = 0

Factor a trinomial.
2((-12 + -1x)(3 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-12, 1.5}

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