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Simplifying 0 = 2y2 + 17y + 30 Reorder the terms: 0 = 30 + 17y + 2y2 Solving 0 = 30 + 17y + 2y2 Solving for variable 'y'. Combine like terms: 0 + -30 = -30 -30 + -17y + -2y2 = 30 + 17y + 2y2 + -30 + -17y + -2y2 Reorder the terms: -30 + -17y + -2y2 = 30 + -30 + 17y + -17y + 2y2 + -2y2 Combine like terms: 30 + -30 = 0 -30 + -17y + -2y2 = 0 + 17y + -17y + 2y2 + -2y2 -30 + -17y + -2y2 = 17y + -17y + 2y2 + -2y2 Combine like terms: 17y + -17y = 0 -30 + -17y + -2y2 = 0 + 2y2 + -2y2 -30 + -17y + -2y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 -30 + -17y + -2y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(30 + 17y + 2y2) = 0 Factor a trinomial. -1((6 + y)(5 + 2y)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + y)' equal to zero and attempt to solve: Simplifying 6 + y = 0 Solving 6 + y = 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 + y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + y = 0 + -6 y = 0 + -6 Combine like terms: 0 + -6 = -6 y = -6 Simplifying y = -6Subproblem 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 = -2.5Solution
y = {-6, -2.5}
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