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Simplifying 0 = 3x3 + 24x2 + 48x Reorder the terms: 0 = 48x + 24x2 + 3x3 Solving 0 = 48x + 24x2 + 3x3 Solving for variable 'x'. Remove the zero: -48x + -24x2 + -3x3 = 48x + 24x2 + 3x3 + -48x + -24x2 + -3x3 Reorder the terms: -48x + -24x2 + -3x3 = 48x + -48x + 24x2 + -24x2 + 3x3 + -3x3 Combine like terms: 48x + -48x = 0 -48x + -24x2 + -3x3 = 0 + 24x2 + -24x2 + 3x3 + -3x3 -48x + -24x2 + -3x3 = 24x2 + -24x2 + 3x3 + -3x3 Combine like terms: 24x2 + -24x2 = 0 -48x + -24x2 + -3x3 = 0 + 3x3 + -3x3 -48x + -24x2 + -3x3 = 3x3 + -3x3 Combine like terms: 3x3 + -3x3 = 0 -48x + -24x2 + -3x3 = 0 Factor out the Greatest Common Factor (GCF), '-3x'. -3x(16 + 8x + x2) = 0 Factor a trinomial. -3x((4 + x)(4 + x)) = 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {0, -4, -4}
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