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Simplifying 0 = -3x3 + 24x2 + 27x Reorder the terms: 0 = 27x + 24x2 + -3x3 Solving 0 = 27x + 24x2 + -3x3 Solving for variable 'x'. Remove the zero: -27x + -24x2 + 3x3 = 27x + 24x2 + -3x3 + -27x + -24x2 + 3x3 Reorder the terms: -27x + -24x2 + 3x3 = 27x + -27x + 24x2 + -24x2 + -3x3 + 3x3 Combine like terms: 27x + -27x = 0 -27x + -24x2 + 3x3 = 0 + 24x2 + -24x2 + -3x3 + 3x3 -27x + -24x2 + 3x3 = 24x2 + -24x2 + -3x3 + 3x3 Combine like terms: 24x2 + -24x2 = 0 -27x + -24x2 + 3x3 = 0 + -3x3 + 3x3 -27x + -24x2 + 3x3 = -3x3 + 3x3 Combine like terms: -3x3 + 3x3 = 0 -27x + -24x2 + 3x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-9 + -8x + x2) = 0 Factor a trinomial. 3x((-1 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {0, -1, 9}
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