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Simplifying 0 = 5x3 + -45x2 + 40x Reorder the terms: 0 = 40x + -45x2 + 5x3 Solving 0 = 40x + -45x2 + 5x3 Solving for variable 'x'. Remove the zero: -40x + 45x2 + -5x3 = 40x + -45x2 + 5x3 + -40x + 45x2 + -5x3 Reorder the terms: -40x + 45x2 + -5x3 = 40x + -40x + -45x2 + 45x2 + 5x3 + -5x3 Combine like terms: 40x + -40x = 0 -40x + 45x2 + -5x3 = 0 + -45x2 + 45x2 + 5x3 + -5x3 -40x + 45x2 + -5x3 = -45x2 + 45x2 + 5x3 + -5x3 Combine like terms: -45x2 + 45x2 = 0 -40x + 45x2 + -5x3 = 0 + 5x3 + -5x3 -40x + 45x2 + -5x3 = 5x3 + -5x3 Combine like terms: 5x3 + -5x3 = 0 -40x + 45x2 + -5x3 = 0 Factor out the Greatest Common Factor (GCF), '5x'. 5x(-8 + 9x + -1x2) = 0 Factor a trinomial. 5x((-8 + x)(1 + -1x)) = 0 Ignore the factor 5.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 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 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 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8Subproblem 3
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 = 1Solution
x = {0, 8, 1}
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