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

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


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

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

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

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

Combine like terms: -6x + -2x = -8x
x(2 + -8x + 6x2) = 0
(2 * x + -8x * x + 6x2 * x) = 0
(2x + -8x2 + 6x3) = 0

Solving
2x + -8x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(1 + -4x + 3x2) = 0

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

Ignore the factor 2.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, 0.3333333333, 1}

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