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Simplifying x(x + -2)(x + -3) = 0 Reorder the terms: x(-2 + x)(x + -3) = 0 Reorder the terms: x(-2 + x)(-3 + x) = 0 Multiply (-2 + x) * (-3 + x) x(-2(-3 + x) + x(-3 + x)) = 0 x((-3 * -2 + x * -2) + x(-3 + x)) = 0 x((6 + -2x) + x(-3 + x)) = 0 x(6 + -2x + (-3 * x + x * x)) = 0 x(6 + -2x + (-3x + x2)) = 0 Combine like terms: -2x + -3x = -5x x(6 + -5x + x2) = 0 (6 * x + -5x * x + x2 * x) = 0 (6x + -5x2 + x3) = 0 Solving 6x + -5x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(6 + -5x + x2) = 0 Factor a trinomial. x((2 + -1x)(3 + -1x)) = 0Subproblem 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 '(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 = 2Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {0, 2, 3}
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