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Simplifying 5y3 + -11y2 = 2y2 + 6y Reorder the terms: -11y2 + 5y3 = 2y2 + 6y Reorder the terms: -11y2 + 5y3 = 6y + 2y2 Solving -11y2 + 5y3 = 6y + 2y2 Solving for variable 'y'. Reorder the terms: -6y + -11y2 + -2y2 + 5y3 = 6y + 2y2 + -6y + -2y2 Combine like terms: -11y2 + -2y2 = -13y2 -6y + -13y2 + 5y3 = 6y + 2y2 + -6y + -2y2 Reorder the terms: -6y + -13y2 + 5y3 = 6y + -6y + 2y2 + -2y2 Combine like terms: 6y + -6y = 0 -6y + -13y2 + 5y3 = 0 + 2y2 + -2y2 -6y + -13y2 + 5y3 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 -6y + -13y2 + 5y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(-6 + -13y + 5y2) = 0 Factor a trinomial. y((-2 + -5y)(3 + -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 '(-2 + -5y)' equal to zero and attempt to solve: Simplifying -2 + -5y = 0 Solving -2 + -5y = 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 + -5y = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5y = 0 + 2 -5y = 0 + 2 Combine like terms: 0 + 2 = 2 -5y = 2 Divide each side by '-5'. y = -0.4 Simplifying y = -0.4Subproblem 3
Set the factor '(3 + -1y)' equal to zero and attempt to solve: Simplifying 3 + -1y = 0 Solving 3 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1y = 0 + -3 -1y = 0 + -3 Combine like terms: 0 + -3 = -3 -1y = -3 Divide each side by '-1'. y = 3 Simplifying y = 3Solution
y = {0, -0.4, 3}
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