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Simplifying 0 = 4x3 + 24x2 + 36x Reorder the terms: 0 = 36x + 24x2 + 4x3 Solving 0 = 36x + 24x2 + 4x3 Solving for variable 'x'. Remove the zero: -36x + -24x2 + -4x3 = 36x + 24x2 + 4x3 + -36x + -24x2 + -4x3 Reorder the terms: -36x + -24x2 + -4x3 = 36x + -36x + 24x2 + -24x2 + 4x3 + -4x3 Combine like terms: 36x + -36x = 0 -36x + -24x2 + -4x3 = 0 + 24x2 + -24x2 + 4x3 + -4x3 -36x + -24x2 + -4x3 = 24x2 + -24x2 + 4x3 + -4x3 Combine like terms: 24x2 + -24x2 = 0 -36x + -24x2 + -4x3 = 0 + 4x3 + -4x3 -36x + -24x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 -36x + -24x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), '-4x'. -4x(9 + 6x + x2) = 0 Factor a trinomial. -4x((3 + x)(3 + x)) = 0 Ignore the factor -4.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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 3
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {0, -3, -3}
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