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

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


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

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

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

Multiply (-3 + 2x) * (-4 + 3x)
3x(-3(-4 + 3x) + 2x * (-4 + 3x)) = 0
3x((-4 * -3 + 3x * -3) + 2x * (-4 + 3x)) = 0
3x((12 + -9x) + 2x * (-4 + 3x)) = 0
3x(12 + -9x + (-4 * 2x + 3x * 2x)) = 0
3x(12 + -9x + (-8x + 6x2)) = 0

Combine like terms: -9x + -8x = -17x
3x(12 + -17x + 6x2) = 0
(12 * 3x + -17x * 3x + 6x2 * 3x) = 0
(36x + -51x2 + 18x3) = 0

Solving
36x + -51x2 + 18x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(12 + -17x + 6x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 3
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 = {0, 1.333333333, 1.5}

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