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 + x2) = 0

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

Subproblem 3

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {0, 1, 2}

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