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Simplifying 0 = 4x3 + 32x2 + 48x Reorder the terms: 0 = 48x + 32x2 + 4x3 Solving 0 = 48x + 32x2 + 4x3 Solving for variable 'x'. Remove the zero: -48x + -32x2 + -4x3 = 48x + 32x2 + 4x3 + -48x + -32x2 + -4x3 Reorder the terms: -48x + -32x2 + -4x3 = 48x + -48x + 32x2 + -32x2 + 4x3 + -4x3 Combine like terms: 48x + -48x = 0 -48x + -32x2 + -4x3 = 0 + 32x2 + -32x2 + 4x3 + -4x3 -48x + -32x2 + -4x3 = 32x2 + -32x2 + 4x3 + -4x3 Combine like terms: 32x2 + -32x2 = 0 -48x + -32x2 + -4x3 = 0 + 4x3 + -4x3 -48x + -32x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 -48x + -32x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), '-4x'. -4x(12 + 8x + x2) = 0 Factor a trinomial. -4x((6 + x)(2 + 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {0, -6, -2}
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