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

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


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

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

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

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

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

Solving
-108 + 3x + 6x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-4.5, 4}

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