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

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


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

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

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

Multiply (12 + 3x) * (-3 + 2x)
(12(-3 + 2x) + 3x * (-3 + 2x)) = 0
((-3 * 12 + 2x * 12) + 3x * (-3 + 2x)) = 0
((-36 + 24x) + 3x * (-3 + 2x)) = 0
(-36 + 24x + (-3 * 3x + 2x * 3x)) = 0
(-36 + 24x + (-9x + 6x2)) = 0

Combine like terms: 24x + -9x = 15x
(-36 + 15x + 6x2) = 0

Solving
-36 + 15x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 5x + 2x2) = 0

Factor a trinomial.
3((-4 + -1x)(3 + -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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-4, 1.5}

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