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Simplifying 0 = 3y2 + 19y + 20 Reorder the terms: 0 = 20 + 19y + 3y2 Solving 0 = 20 + 19y + 3y2 Solving for variable 'y'. Combine like terms: 0 + -20 = -20 -20 + -19y + -3y2 = 20 + 19y + 3y2 + -20 + -19y + -3y2 Reorder the terms: -20 + -19y + -3y2 = 20 + -20 + 19y + -19y + 3y2 + -3y2 Combine like terms: 20 + -20 = 0 -20 + -19y + -3y2 = 0 + 19y + -19y + 3y2 + -3y2 -20 + -19y + -3y2 = 19y + -19y + 3y2 + -3y2 Combine like terms: 19y + -19y = 0 -20 + -19y + -3y2 = 0 + 3y2 + -3y2 -20 + -19y + -3y2 = 3y2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 -20 + -19y + -3y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(20 + 19y + 3y2) = 0 Factor a trinomial. -1((5 + y)(4 + 3y)) = 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 '(4 + 3y)' equal to zero and attempt to solve: Simplifying 4 + 3y = 0 Solving 4 + 3y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3y = 0 + -4 3y = 0 + -4 Combine like terms: 0 + -4 = -4 3y = -4 Divide each side by '3'. y = -1.333333333 Simplifying y = -1.333333333Solution
y = {-5, -1.333333333}
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