3(x-4)(2x-3)=0

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Solution for 3(x-4)(2x-3)=0 equation: 


Simplifying
3(x + -4)(2x + -3) = 0

Reorder the terms:
3(-4 + x)(2x + -3) = 0

Reorder the terms:
3(-4 + x)(-3 + 2x) = 0

Multiply (-4 + x) * (-3 + 2x)
3(-4(-3 + 2x) + x(-3 + 2x)) = 0
3((-3 * -4 + 2x * -4) + x(-3 + 2x)) = 0
3((12 + -8x) + x(-3 + 2x)) = 0
3(12 + -8x + (-3 * x + 2x * x)) = 0
3(12 + -8x + (-3x + 2x2)) = 0

Combine like terms: -8x + -3x = -11x
3(12 + -11x + 2x2) = 0
(12 * 3 + -11x * 3 + 2x2 * 3) = 0
(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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