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Simplifying 5y3 + -8y2 = 6y2 + 24y Reorder the terms: -8y2 + 5y3 = 6y2 + 24y Reorder the terms: -8y2 + 5y3 = 24y + 6y2 Solving -8y2 + 5y3 = 24y + 6y2 Solving for variable 'y'. Reorder the terms: -24y + -8y2 + -6y2 + 5y3 = 24y + 6y2 + -24y + -6y2 Combine like terms: -8y2 + -6y2 = -14y2 -24y + -14y2 + 5y3 = 24y + 6y2 + -24y + -6y2 Reorder the terms: -24y + -14y2 + 5y3 = 24y + -24y + 6y2 + -6y2 Combine like terms: 24y + -24y = 0 -24y + -14y2 + 5y3 = 0 + 6y2 + -6y2 -24y + -14y2 + 5y3 = 6y2 + -6y2 Combine like terms: 6y2 + -6y2 = 0 -24y + -14y2 + 5y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(-24 + -14y + 5y2) = 0 Factor a trinomial. y((-6 + -5y)(4 + -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 '(-6 + -5y)' equal to zero and attempt to solve: Simplifying -6 + -5y = 0 Solving -6 + -5y = 0 Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -5y = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5y = 0 + 6 -5y = 0 + 6 Combine like terms: 0 + 6 = 6 -5y = 6 Divide each side by '-5'. y = -1.2 Simplifying y = -1.2Subproblem 3
Set the factor '(4 + -1y)' equal to zero and attempt to solve: Simplifying 4 + -1y = 0 Solving 4 + -1y = 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 + -1y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1y = 0 + -4 -1y = 0 + -4 Combine like terms: 0 + -4 = -4 -1y = -4 Divide each side by '-1'. y = 4 Simplifying y = 4Solution
y = {0, -1.2, 4}
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