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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 = 0Subproblem 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 = 1Subproblem 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 = 2Solution
x = {0, 1, 2}
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