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Simplifying 0 = x3 + 14x2 + 45x Reorder the terms: 0 = 45x + 14x2 + x3 Solving 0 = 45x + 14x2 + x3 Solving for variable 'x'. Remove the zero: -45x + -14x2 + -1x3 = 45x + 14x2 + x3 + -45x + -14x2 + -1x3 Reorder the terms: -45x + -14x2 + -1x3 = 45x + -45x + 14x2 + -14x2 + x3 + -1x3 Combine like terms: 45x + -45x = 0 -45x + -14x2 + -1x3 = 0 + 14x2 + -14x2 + x3 + -1x3 -45x + -14x2 + -1x3 = 14x2 + -14x2 + x3 + -1x3 Combine like terms: 14x2 + -14x2 = 0 -45x + -14x2 + -1x3 = 0 + x3 + -1x3 -45x + -14x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -45x + -14x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), '-1x'. -1x(45 + 14x + x2) = 0 Factor a trinomial. -1x((9 + x)(5 + x)) = 0 Ignore the factor -1.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 '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 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 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Subproblem 3
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {0, -9, -5}
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