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Simplifying 54x3 + -24x2 + -64x = 0 Reorder the terms: -64x + -24x2 + 54x3 = 0 Solving -64x + -24x2 + 54x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-32 + -12x + 27x2) = 0 Factor a trinomial. 2x((-8 + -9x)(4 + -3x)) = 0 Ignore the factor 2.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 '(-8 + -9x)' equal to zero and attempt to solve: Simplifying -8 + -9x = 0 Solving -8 + -9x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -9x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -9x = 0 + 8 -9x = 0 + 8 Combine like terms: 0 + 8 = 8 -9x = 8 Divide each side by '-9'. x = -0.8888888889 Simplifying x = -0.8888888889Subproblem 3
Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Solution
x = {0, -0.8888888889, 1.333333333}
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