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Simplifying 2y3 + -3y2 = 4y2 + 30y Reorder the terms: -3y2 + 2y3 = 4y2 + 30y Reorder the terms: -3y2 + 2y3 = 30y + 4y2 Solving -3y2 + 2y3 = 30y + 4y2 Solving for variable 'y'. Reorder the terms: -30y + -3y2 + -4y2 + 2y3 = 30y + 4y2 + -30y + -4y2 Combine like terms: -3y2 + -4y2 = -7y2 -30y + -7y2 + 2y3 = 30y + 4y2 + -30y + -4y2 Reorder the terms: -30y + -7y2 + 2y3 = 30y + -30y + 4y2 + -4y2 Combine like terms: 30y + -30y = 0 -30y + -7y2 + 2y3 = 0 + 4y2 + -4y2 -30y + -7y2 + 2y3 = 4y2 + -4y2 Combine like terms: 4y2 + -4y2 = 0 -30y + -7y2 + 2y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(-30 + -7y + 2y2) = 0 Factor a trinomial. y((-5 + -2y)(6 + -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 '(-5 + -2y)' equal to zero and attempt to solve: Simplifying -5 + -2y = 0 Solving -5 + -2y = 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 + -2y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2y = 0 + 5 -2y = 0 + 5 Combine like terms: 0 + 5 = 5 -2y = 5 Divide each side by '-2'. y = -2.5 Simplifying y = -2.5Subproblem 3
Set the factor '(6 + -1y)' equal to zero and attempt to solve: Simplifying 6 + -1y = 0 Solving 6 + -1y = 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 + -1y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1y = 0 + -6 -1y = 0 + -6 Combine like terms: 0 + -6 = -6 -1y = -6 Divide each side by '-1'. y = 6 Simplifying y = 6Solution
y = {0, -2.5, 6}
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