0=2(x+12)(x-9)

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Solution for 0=2(x+12)(x-9) equation: 


Simplifying
0 = 2(x + 12)(x + -9)

Reorder the terms:
0 = 2(12 + x)(x + -9)

Reorder the terms:
0 = 2(12 + x)(-9 + x)

Multiply (12 + x) * (-9 + x)
0 = 2(12(-9 + x) + x(-9 + x))
0 = 2((-9 * 12 + x * 12) + x(-9 + x))
0 = 2((-108 + 12x) + x(-9 + x))
0 = 2(-108 + 12x + (-9 * x + x * x))
0 = 2(-108 + 12x + (-9x + x2))

Combine like terms: 12x + -9x = 3x
0 = 2(-108 + 3x + x2)
0 = (-108 * 2 + 3x * 2 + x2 * 2)
0 = (-216 + 6x + 2x2)

Solving
0 = -216 + 6x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 216 = 216
216 + -6x + -2x2 = -216 + 6x + 2x2 + 216 + -6x + -2x2

Reorder the terms:
216 + -6x + -2x2 = -216 + 216 + 6x + -6x + 2x2 + -2x2

Combine like terms: -216 + 216 = 0
216 + -6x + -2x2 = 0 + 6x + -6x + 2x2 + -2x2
216 + -6x + -2x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
216 + -6x + -2x2 = 0 + 2x2 + -2x2
216 + -6x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
216 + -6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(108 + -3x + -1x2) = 0

Factor a trinomial.
2((9 + -1x)(12 + x)) = 0

Ignore the factor 2.

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 '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 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 + x = 0 + -12

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

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

Simplifying
x = -12
Solution
x = {9, -12}

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