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

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


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

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

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

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

Combine like terms: -2x + -3x = -5x
x(2 + -5x + 3x2) = 0
(2 * x + -5x * x + 3x2 * x) = 0
(2x + -5x2 + 3x3) = 0

Solving
2x + -5x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(2 + -5x + 3x2) = 0

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


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 '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

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, 0.6666666667, 1}

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