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

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


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

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

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

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

Combine like terms: -9x + -24x = -33x
(36 + -33x + 6x2) = 0

Solving
36 + -33x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -11x + 2x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

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 = {1.5, 4}

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