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Simplifying 0 = 2y2 + 13y + 15 Reorder the terms: 0 = 15 + 13y + 2y2 Solving 0 = 15 + 13y + 2y2 Solving for variable 'y'. Combine like terms: 0 + -15 = -15 -15 + -13y + -2y2 = 15 + 13y + 2y2 + -15 + -13y + -2y2 Reorder the terms: -15 + -13y + -2y2 = 15 + -15 + 13y + -13y + 2y2 + -2y2 Combine like terms: 15 + -15 = 0 -15 + -13y + -2y2 = 0 + 13y + -13y + 2y2 + -2y2 -15 + -13y + -2y2 = 13y + -13y + 2y2 + -2y2 Combine like terms: 13y + -13y = 0 -15 + -13y + -2y2 = 0 + 2y2 + -2y2 -15 + -13y + -2y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 -15 + -13y + -2y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 13y + 2y2) = 0 Factor a trinomial. -1((5 + y)(3 + 2y)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + y)' equal to zero and attempt to solve: Simplifying 5 + y = 0 Solving 5 + y = 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 + y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + y = 0 + -5 y = 0 + -5 Combine like terms: 0 + -5 = -5 y = -5 Simplifying y = -5Subproblem 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 = -1.5Solution
y = {-5, -1.5}
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