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Simplifying 0 = 9x3 + -3x2 + -30x Reorder the terms: 0 = -30x + -3x2 + 9x3 Solving 0 = -30x + -3x2 + 9x3 Solving for variable 'x'. Remove the zero: 30x + 3x2 + -9x3 = -30x + -3x2 + 9x3 + 30x + 3x2 + -9x3 Reorder the terms: 30x + 3x2 + -9x3 = -30x + 30x + -3x2 + 3x2 + 9x3 + -9x3 Combine like terms: -30x + 30x = 0 30x + 3x2 + -9x3 = 0 + -3x2 + 3x2 + 9x3 + -9x3 30x + 3x2 + -9x3 = -3x2 + 3x2 + 9x3 + -9x3 Combine like terms: -3x2 + 3x2 = 0 30x + 3x2 + -9x3 = 0 + 9x3 + -9x3 30x + 3x2 + -9x3 = 9x3 + -9x3 Combine like terms: 9x3 + -9x3 = 0 30x + 3x2 + -9x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(10 + x + -3x2) = 0 Factor a trinomial. 3x((2 + -1x)(5 + 3x)) = 0 Ignore the factor 3.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 '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 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 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667Solution
x = {0, 2, -1.666666667}
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