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Simplifying 9y3 = -9y2 + 10y Reorder the terms: 9y3 = 10y + -9y2 Solving 9y3 = 10y + -9y2 Solving for variable 'y'. Reorder the terms: -10y + 9y2 + 9y3 = 10y + -9y2 + -10y + 9y2 Reorder the terms: -10y + 9y2 + 9y3 = 10y + -10y + -9y2 + 9y2 Combine like terms: 10y + -10y = 0 -10y + 9y2 + 9y3 = 0 + -9y2 + 9y2 -10y + 9y2 + 9y3 = -9y2 + 9y2 Combine like terms: -9y2 + 9y2 = 0 -10y + 9y2 + 9y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(-10 + 9y + 9y2) = 0 Factor a trinomial. y((-5 + -3y)(2 + -3y)) = 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 '(-5 + -3y)' equal to zero and attempt to solve: Simplifying -5 + -3y = 0 Solving -5 + -3y = 0 Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -3y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3y = 0 + 5 -3y = 0 + 5 Combine like terms: 0 + 5 = 5 -3y = 5 Divide each side by '-3'. y = -1.666666667 Simplifying y = -1.666666667Subproblem 3
Set the factor '(2 + -3y)' equal to zero and attempt to solve: Simplifying 2 + -3y = 0 Solving 2 + -3y = 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 + -3y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3y = 0 + -2 -3y = 0 + -2 Combine like terms: 0 + -2 = -2 -3y = -2 Divide each side by '-3'. y = 0.6666666667 Simplifying y = 0.6666666667Solution
y = {0, -1.666666667, 0.6666666667}
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