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

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


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

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

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

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

Combine like terms: -1x + -2x = -3x
-3x(2 + -3x + x2) = 0
(2 * -3x + -3x * -3x + x2 * -3x) = 0
(-6x + 9x2 + -3x3) = 0

Solving
-6x + 9x2 + -3x3 = 0

Solving for variable 'x'.

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

Factor a trinomial.
3x((-2 + x)(1 + -1x)) = 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 '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 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 + x = 0 + 2

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

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

Simplifying
x = 2

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, 2, 1}

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