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Simplifying 0 = x3 + 6x2 + -135x Reorder the terms: 0 = -135x + 6x2 + x3 Solving 0 = -135x + 6x2 + x3 Solving for variable 'x'. Remove the zero: 135x + -6x2 + -1x3 = -135x + 6x2 + x3 + 135x + -6x2 + -1x3 Reorder the terms: 135x + -6x2 + -1x3 = -135x + 135x + 6x2 + -6x2 + x3 + -1x3 Combine like terms: -135x + 135x = 0 135x + -6x2 + -1x3 = 0 + 6x2 + -6x2 + x3 + -1x3 135x + -6x2 + -1x3 = 6x2 + -6x2 + x3 + -1x3 Combine like terms: 6x2 + -6x2 = 0 135x + -6x2 + -1x3 = 0 + x3 + -1x3 135x + -6x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 135x + -6x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(135 + -6x + -1x2) = 0 Factor a trinomial. x((9 + -1x)(15 + x)) = 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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Subproblem 3
Set the factor '(15 + x)' equal to zero and attempt to solve: Simplifying 15 + x = 0 Solving 15 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + x = 0 + -15 x = 0 + -15 Combine like terms: 0 + -15 = -15 x = -15 Simplifying x = -15Solution
x = {0, 9, -15}
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