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Simplifying 0 = 6x3 + -12x2 + -48x Reorder the terms: 0 = -48x + -12x2 + 6x3 Solving 0 = -48x + -12x2 + 6x3 Solving for variable 'x'. Remove the zero: 48x + 12x2 + -6x3 = -48x + -12x2 + 6x3 + 48x + 12x2 + -6x3 Reorder the terms: 48x + 12x2 + -6x3 = -48x + 48x + -12x2 + 12x2 + 6x3 + -6x3 Combine like terms: -48x + 48x = 0 48x + 12x2 + -6x3 = 0 + -12x2 + 12x2 + 6x3 + -6x3 48x + 12x2 + -6x3 = -12x2 + 12x2 + 6x3 + -6x3 Combine like terms: -12x2 + 12x2 = 0 48x + 12x2 + -6x3 = 0 + 6x3 + -6x3 48x + 12x2 + -6x3 = 6x3 + -6x3 Combine like terms: 6x3 + -6x3 = 0 48x + 12x2 + -6x3 = 0 Factor out the Greatest Common Factor (GCF), '6x'. 6x(8 + 2x + -1x2) = 0 Factor a trinomial. 6x((4 + -1x)(2 + x)) = 0 Ignore the factor 6.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 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 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, 4, -2}
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