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Simplifying y3 + 8y2 = 20y Reorder the terms: 8y2 + y3 = 20y Solving 8y2 + y3 = 20y Solving for variable 'y'. Reorder the terms: -20y + 8y2 + y3 = 20y + -20y Combine like terms: 20y + -20y = 0 -20y + 8y2 + y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(-20 + 8y + y2) = 0 Factor a trinomial. y((-10 + -1y)(2 + -1y)) = 0Subproblem 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 = 0Subproblem 2
Set the factor '(-10 + -1y)' equal to zero and attempt to solve: Simplifying -10 + -1y = 0 Solving -10 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1y = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1y = 0 + 10 -1y = 0 + 10 Combine like terms: 0 + 10 = 10 -1y = 10 Divide each side by '-1'. y = -10 Simplifying y = -10Subproblem 3
Set the factor '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2Solution
y = {0, -10, 2}
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