12(x+3)+12(x-3)=3(x^2-9)

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Solution for 12(x+3)+12(x-3)=3(x^2-9) equation: 


Simplifying
12(x + 3) + 12(x + -3) = 3(x2 + -9)

Reorder the terms:
12(3 + x) + 12(x + -3) = 3(x2 + -9)
(3 * 12 + x * 12) + 12(x + -3) = 3(x2 + -9)
(36 + 12x) + 12(x + -3) = 3(x2 + -9)

Reorder the terms:
36 + 12x + 12(-3 + x) = 3(x2 + -9)
36 + 12x + (-3 * 12 + x * 12) = 3(x2 + -9)
36 + 12x + (-36 + 12x) = 3(x2 + -9)

Reorder the terms:
36 + -36 + 12x + 12x = 3(x2 + -9)

Combine like terms: 36 + -36 = 0
0 + 12x + 12x = 3(x2 + -9)
12x + 12x = 3(x2 + -9)

Combine like terms: 12x + 12x = 24x
24x = 3(x2 + -9)

Reorder the terms:
24x = 3(-9 + x2)
24x = (-9 * 3 + x2 * 3)
24x = (-27 + 3x2)

Solving
24x = -27 + 3x2

Solving for variable 'x'.

Reorder the terms:
27 + 24x + -3x2 = -27 + 3x2 + 27 + -3x2

Reorder the terms:
27 + 24x + -3x2 = -27 + 27 + 3x2 + -3x2

Combine like terms: -27 + 27 = 0
27 + 24x + -3x2 = 0 + 3x2 + -3x2
27 + 24x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
27 + 24x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 8x + -1x2) = 0

Factor a trinomial.
3((9 + -1x)(1 + x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {9, -1}

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