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Simplifying y^{3}+ 8y^{2}+ 16y = 0 Reorder the terms: 16y + 8y^{2}+ y^{3}= 0 Solving 16y + 8y^{2}+ y^{3}= 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(16 + 8y + y^{2}) = 0 Factor a trinomial. y((4 + y)(4 + y)) = 0## Subproblem 1

Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0## Subproblem 2

Set the factor '(4 + y)' equal to zero and attempt to solve: Simplifying 4 + y = 0 Solving 4 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + y = 0 + -4 y = 0 + -4 Combine like terms: 0 + -4 = -4 y = -4 Simplifying y = -4## Subproblem 3

Set the factor '(4 + y)' equal to zero and attempt to solve: Simplifying 4 + y = 0 Solving 4 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + y = 0 + -4 y = 0 + -4 Combine like terms: 0 + -4 = -4 y = -4 Simplifying y = -4## Solution

y = {0, -4, -4}

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