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Simplifying 0 = x3 + -9x2 + 20x Reorder the terms: 0 = 20x + -9x2 + x3 Solving 0 = 20x + -9x2 + x3 Solving for variable 'x'. Remove the zero: -20x + 9x2 + -1x3 = 20x + -9x2 + x3 + -20x + 9x2 + -1x3 Reorder the terms: -20x + 9x2 + -1x3 = 20x + -20x + -9x2 + 9x2 + x3 + -1x3 Combine like terms: 20x + -20x = 0 -20x + 9x2 + -1x3 = 0 + -9x2 + 9x2 + x3 + -1x3 -20x + 9x2 + -1x3 = -9x2 + 9x2 + x3 + -1x3 Combine like terms: -9x2 + 9x2 = 0 -20x + 9x2 + -1x3 = 0 + x3 + -1x3 -20x + 9x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -20x + 9x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-20 + 9x + -1x2) = 0 Factor a trinomial. x((-5 + x)(4 + -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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {0, 5, 4}
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