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Simplifying 3x(x + -2)(2x + 1) = 0 Reorder the terms: 3x(-2 + x)(2x + 1) = 0 Reorder the terms: 3x(-2 + x)(1 + 2x) = 0 Multiply (-2 + x) * (1 + 2x) 3x(-2(1 + 2x) + x(1 + 2x)) = 0 3x((1 * -2 + 2x * -2) + x(1 + 2x)) = 0 3x((-2 + -4x) + x(1 + 2x)) = 0 3x(-2 + -4x + (1 * x + 2x * x)) = 0 3x(-2 + -4x + (1x + 2x2)) = 0 Combine like terms: -4x + 1x = -3x 3x(-2 + -3x + 2x2) = 0 (-2 * 3x + -3x * 3x + 2x2 * 3x) = 0 (-6x + -9x2 + 6x3) = 0 Solving -6x + -9x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(-2 + -3x + 2x2) = 0 Factor a trinomial. 3x((-1 + -2x)(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 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 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, -0.5, 2}
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