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Simplifying 0 = 9x2 + 6x + -27x3 Reorder the terms: 0 = 6x + 9x2 + -27x3 Solving 0 = 6x + 9x2 + -27x3 Solving for variable 'x'. Remove the zero: -6x + -9x2 + 27x3 = 6x + 9x2 + -27x3 + -6x + -9x2 + 27x3 Reorder the terms: -6x + -9x2 + 27x3 = 6x + -6x + 9x2 + -9x2 + -27x3 + 27x3 Combine like terms: 6x + -6x = 0 -6x + -9x2 + 27x3 = 0 + 9x2 + -9x2 + -27x3 + 27x3 -6x + -9x2 + 27x3 = 9x2 + -9x2 + -27x3 + 27x3 Combine like terms: 9x2 + -9x2 = 0 -6x + -9x2 + 27x3 = 0 + -27x3 + 27x3 -6x + -9x2 + 27x3 = -27x3 + 27x3 Combine like terms: -27x3 + 27x3 = 0 -6x + -9x2 + 27x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-2 + -3x + 9x2) = 0 Factor a trinomial. 3x((-1 + -3x)(2 + -3x)) = 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 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 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 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333Subproblem 3
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {0, -0.3333333333, 0.6666666667}
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