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Simplifying 0 = -2x5 + 2x4 + 40x3 Reorder the terms: 0 = 40x3 + 2x4 + -2x5 Solving 0 = 40x3 + 2x4 + -2x5 Solving for variable 'x'. Remove the zero: -40x3 + -2x4 + 2x5 = 40x3 + 2x4 + -2x5 + -40x3 + -2x4 + 2x5 Reorder the terms: -40x3 + -2x4 + 2x5 = 40x3 + -40x3 + 2x4 + -2x4 + -2x5 + 2x5 Combine like terms: 40x3 + -40x3 = 0 -40x3 + -2x4 + 2x5 = 0 + 2x4 + -2x4 + -2x5 + 2x5 -40x3 + -2x4 + 2x5 = 2x4 + -2x4 + -2x5 + 2x5 Combine like terms: 2x4 + -2x4 = 0 -40x3 + -2x4 + 2x5 = 0 + -2x5 + 2x5 -40x3 + -2x4 + 2x5 = -2x5 + 2x5 Combine like terms: -2x5 + 2x5 = 0 -40x3 + -2x4 + 2x5 = 0 Factor out the Greatest Common Factor (GCF), '2x3'. 2x3(-20 + -1x + x2) = 0 Factor a trinomial. 2x3((-4 + -1x)(5 + -1x)) = 0 Ignore the factor 2.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 '(-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 = -4Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-4, 5}
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