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Simplifying x5 + 4x3 = 5x4 + -2x3 Reorder the terms: 4x3 + x5 = 5x4 + -2x3 Reorder the terms: 4x3 + x5 = -2x3 + 5x4 Solving 4x3 + x5 = -2x3 + 5x4 Solving for variable 'x'. Reorder the terms: 4x3 + 2x3 + -5x4 + x5 = -2x3 + 5x4 + 2x3 + -5x4 Combine like terms: 4x3 + 2x3 = 6x3 6x3 + -5x4 + x5 = -2x3 + 5x4 + 2x3 + -5x4 Reorder the terms: 6x3 + -5x4 + x5 = -2x3 + 2x3 + 5x4 + -5x4 Combine like terms: -2x3 + 2x3 = 0 6x3 + -5x4 + x5 = 0 + 5x4 + -5x4 6x3 + -5x4 + x5 = 5x4 + -5x4 Combine like terms: 5x4 + -5x4 = 0 6x3 + -5x4 + x5 = 0 Factor out the Greatest Common Factor (GCF), 'x3'. x3(6 + -5x + x2) = 0 Factor a trinomial. x3((2 + -1x)(3 + -1x)) = 0Subproblem 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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