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Simplifying x3 = 6x2 + 16x Reorder the terms: x3 = 16x + 6x2 Solving x3 = 16x + 6x2 Solving for variable 'x'. Reorder the terms: -16x + -6x2 + x3 = 16x + 6x2 + -16x + -6x2 Reorder the terms: -16x + -6x2 + x3 = 16x + -16x + 6x2 + -6x2 Combine like terms: 16x + -16x = 0 -16x + -6x2 + x3 = 0 + 6x2 + -6x2 -16x + -6x2 + x3 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -16x + -6x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-16 + -6x + x2) = 0 Factor a trinomial. x((-2 + -1x)(8 + -1x)) = 0Subproblem 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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {0, -2, 8}
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