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