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Simplifying 2y3 + -4y2 = 3y2 + 15y Reorder the terms: -4y2 + 2y3 = 3y2 + 15y Reorder the terms: -4y2 + 2y3 = 15y + 3y2 Solving -4y2 + 2y3 = 15y + 3y2 Solving for variable 'y'. Reorder the terms: -15y + -4y2 + -3y2 + 2y3 = 15y + 3y2 + -15y + -3y2 Combine like terms: -4y2 + -3y2 = -7y2 -15y + -7y2 + 2y3 = 15y + 3y2 + -15y + -3y2 Reorder the terms: -15y + -7y2 + 2y3 = 15y + -15y + 3y2 + -3y2 Combine like terms: 15y + -15y = 0 -15y + -7y2 + 2y3 = 0 + 3y2 + -3y2 -15y + -7y2 + 2y3 = 3y2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 -15y + -7y2 + 2y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(-15 + -7y + 2y2) = 0 Factor a trinomial. y((-3 + -2y)(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 '(-3 + -2y)' equal to zero and attempt to solve: Simplifying -3 + -2y = 0 Solving -3 + -2y = 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 + -2y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2y = 0 + 3 -2y = 0 + 3 Combine like terms: 0 + 3 = 3 -2y = 3 Divide each side by '-2'. y = -1.5 Simplifying y = -1.5Subproblem 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, -1.5, 5}
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