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Simplifying 5y3 + -16y2 = 3y2 + 30y Reorder the terms: -16y2 + 5y3 = 3y2 + 30y Reorder the terms: -16y2 + 5y3 = 30y + 3y2 Solving -16y2 + 5y3 = 30y + 3y2 Solving for variable 'y'. Reorder the terms: -30y + -16y2 + -3y2 + 5y3 = 30y + 3y2 + -30y + -3y2 Combine like terms: -16y2 + -3y2 = -19y2 -30y + -19y2 + 5y3 = 30y + 3y2 + -30y + -3y2 Reorder the terms: -30y + -19y2 + 5y3 = 30y + -30y + 3y2 + -3y2 Combine like terms: 30y + -30y = 0 -30y + -19y2 + 5y3 = 0 + 3y2 + -3y2 -30y + -19y2 + 5y3 = 3y2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 -30y + -19y2 + 5y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(-30 + -19y + 5y2) = 0 Factor a trinomial. y((-6 + -5y)(5 + -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 '(5 + -1y)' equal to zero and attempt to solve: Simplifying 5 + -1y = 0 Solving 5 + -1y = 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 + -1y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1y = 0 + -5 -1y = 0 + -5 Combine like terms: 0 + -5 = -5 -1y = -5 Divide each side by '-1'. y = 5 Simplifying y = 5Solution
y = {0, -1.2, 5}
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