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