(3x+12)(3x+12)=9

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Solution for (3x+12)(3x+12)=9 equation: 


Simplifying
(3x + 12)(3x + 12) = 9

Reorder the terms:
(12 + 3x)(3x + 12) = 9

Reorder the terms:
(12 + 3x)(12 + 3x) = 9

Multiply (12 + 3x) * (12 + 3x)
(12(12 + 3x) + 3x * (12 + 3x)) = 9
((12 * 12 + 3x * 12) + 3x * (12 + 3x)) = 9
((144 + 36x) + 3x * (12 + 3x)) = 9
(144 + 36x + (12 * 3x + 3x * 3x)) = 9
(144 + 36x + (36x + 9x2)) = 9

Combine like terms: 36x + 36x = 72x
(144 + 72x + 9x2) = 9

Solving
144 + 72x + 9x2 = 9

Solving for variable 'x'.

Reorder the terms:
144 + -9 + 72x + 9x2 = 9 + -9

Combine like terms: 144 + -9 = 135
135 + 72x + 9x2 = 9 + -9

Combine like terms: 9 + -9 = 0
135 + 72x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(15 + 8x + x2) = 0

Factor a trinomial.
9((5 + x)(3 + x)) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5

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

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {-5, -3}

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