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Simplifying (2x + -1) * x(3x + 9) = 0 Reorder the terms: (-1 + 2x) * x(3x + 9) = 0 Reorder the terms: (-1 + 2x) * x(9 + 3x) = 0 Reorder the terms for easier multiplication: x(-1 + 2x)(9 + 3x) = 0 Multiply (-1 + 2x) * (9 + 3x) x(-1(9 + 3x) + 2x * (9 + 3x)) = 0 x((9 * -1 + 3x * -1) + 2x * (9 + 3x)) = 0 x((-9 + -3x) + 2x * (9 + 3x)) = 0 x(-9 + -3x + (9 * 2x + 3x * 2x)) = 0 x(-9 + -3x + (18x + 6x2)) = 0 Combine like terms: -3x + 18x = 15x x(-9 + 15x + 6x2) = 0 (-9 * x + 15x * x + 6x2 * x) = 0 (-9x + 15x2 + 6x3) = 0 Solving -9x + 15x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(-3 + 5x + 2x2) = 0 Factor a trinomial. 3x((-3 + -1x)(1 + -2x)) = 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 '(-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 = -3Subproblem 3
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 = 0.5Solution
x = {0, -3, 0.5}
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