4x(2x-3)(3x-1)=0

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Solution for 4x(2x-3)(3x-1)=0 equation: 


Simplifying
4x(2x + -3)(3x + -1) = 0

Reorder the terms:
4x(-3 + 2x)(3x + -1) = 0

Reorder the terms:
4x(-3 + 2x)(-1 + 3x) = 0

Multiply (-3 + 2x) * (-1 + 3x)
4x(-3(-1 + 3x) + 2x * (-1 + 3x)) = 0
4x((-1 * -3 + 3x * -3) + 2x * (-1 + 3x)) = 0
4x((3 + -9x) + 2x * (-1 + 3x)) = 0
4x(3 + -9x + (-1 * 2x + 3x * 2x)) = 0
4x(3 + -9x + (-2x + 6x2)) = 0

Combine like terms: -9x + -2x = -11x
4x(3 + -11x + 6x2) = 0
(3 * 4x + -11x * 4x + 6x2 * 4x) = 0
(12x + -44x2 + 24x3) = 0

Solving
12x + -44x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(3 + -11x + 6x2) = 0

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

Ignore the factor 4.

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 '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

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, 0.3333333333, 1.5}

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