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Simplifying 0 = 5x3 + -5x2 + -10x Reorder the terms: 0 = -10x + -5x2 + 5x3 Solving 0 = -10x + -5x2 + 5x3 Solving for variable 'x'. Remove the zero: 10x + 5x2 + -5x3 = -10x + -5x2 + 5x3 + 10x + 5x2 + -5x3 Reorder the terms: 10x + 5x2 + -5x3 = -10x + 10x + -5x2 + 5x2 + 5x3 + -5x3 Combine like terms: -10x + 10x = 0 10x + 5x2 + -5x3 = 0 + -5x2 + 5x2 + 5x3 + -5x3 10x + 5x2 + -5x3 = -5x2 + 5x2 + 5x3 + -5x3 Combine like terms: -5x2 + 5x2 = 0 10x + 5x2 + -5x3 = 0 + 5x3 + -5x3 10x + 5x2 + -5x3 = 5x3 + -5x3 Combine like terms: 5x3 + -5x3 = 0 10x + 5x2 + -5x3 = 0 Factor out the Greatest Common Factor (GCF), '5x'. 5x(2 + x + -1x2) = 0 Factor a trinomial. 5x((2 + -1x)(1 + x)) = 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 '(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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {0, 2, -1}
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