(2x-9)(3x+12)=0

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Solution for (2x-9)(3x+12)=0 equation: 


Simplifying
(2x + -9)(3x + 12) = 0

Reorder the terms:
(-9 + 2x)(3x + 12) = 0

Reorder the terms:
(-9 + 2x)(12 + 3x) = 0

Multiply (-9 + 2x) * (12 + 3x)
(-9(12 + 3x) + 2x * (12 + 3x)) = 0
((12 * -9 + 3x * -9) + 2x * (12 + 3x)) = 0
((-108 + -27x) + 2x * (12 + 3x)) = 0
(-108 + -27x + (12 * 2x + 3x * 2x)) = 0
(-108 + -27x + (24x + 6x2)) = 0

Combine like terms: -27x + 24x = -3x
(-108 + -3x + 6x2) = 0

Solving
-108 + -3x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-36 + -1x + 2x2) = 0

Factor a trinomial.
3((-4 + -1x)(9 + -2x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 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 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {-4, 4.5}

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