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Simplifying 10x5 = 10x4 + 60x3 Reorder the terms: 10x5 = 60x3 + 10x4 Solving 10x5 = 60x3 + 10x4 Solving for variable 'x'. Reorder the terms: -60x3 + -10x4 + 10x5 = 60x3 + 10x4 + -60x3 + -10x4 Reorder the terms: -60x3 + -10x4 + 10x5 = 60x3 + -60x3 + 10x4 + -10x4 Combine like terms: 60x3 + -60x3 = 0 -60x3 + -10x4 + 10x5 = 0 + 10x4 + -10x4 -60x3 + -10x4 + 10x5 = 10x4 + -10x4 Combine like terms: 10x4 + -10x4 = 0 -60x3 + -10x4 + 10x5 = 0 Factor out the Greatest Common Factor (GCF), '10x3'. 10x3(-6 + -1x + x2) = 0 Factor a trinomial. 10x3((-2 + -1x)(3 + -1x)) = 0 Ignore the factor 10.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 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 = {-2, 3}
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