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Simplifying x3 + -13x + 3x = -1x3 + 13x2 + -3x Reorder the terms: -13x + 3x + x3 = -1x3 + 13x2 + -3x Combine like terms: -13x + 3x = -10x -10x + x3 = -1x3 + 13x2 + -3x Reorder the terms: -10x + x3 = -3x + 13x2 + -1x3 Solving -10x + x3 = -3x + 13x2 + -1x3 Solving for variable 'x'. Reorder the terms: -10x + 3x + -13x2 + x3 + x3 = -3x + 13x2 + -1x3 + 3x + -13x2 + x3 Combine like terms: -10x + 3x = -7x -7x + -13x2 + x3 + x3 = -3x + 13x2 + -1x3 + 3x + -13x2 + x3 Combine like terms: x3 + x3 = 2x3 -7x + -13x2 + 2x3 = -3x + 13x2 + -1x3 + 3x + -13x2 + x3 Reorder the terms: -7x + -13x2 + 2x3 = -3x + 3x + 13x2 + -13x2 + -1x3 + x3 Combine like terms: -3x + 3x = 0 -7x + -13x2 + 2x3 = 0 + 13x2 + -13x2 + -1x3 + x3 -7x + -13x2 + 2x3 = 13x2 + -13x2 + -1x3 + x3 Combine like terms: 13x2 + -13x2 = 0 -7x + -13x2 + 2x3 = 0 + -1x3 + x3 -7x + -13x2 + 2x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -7x + -13x2 + 2x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-7 + -13x + 2x2) = 0 Factor a trinomial. x((-1 + -2x)(7 + -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 '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 3
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {0, -0.5, 7}
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