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Simplifying (3y + 5)(y + 6) = -3(3y + 5) Reorder the terms: (5 + 3y)(y + 6) = -3(3y + 5) Reorder the terms: (5 + 3y)(6 + y) = -3(3y + 5) Multiply (5 + 3y) * (6 + y) (5(6 + y) + 3y * (6 + y)) = -3(3y + 5) ((6 * 5 + y * 5) + 3y * (6 + y)) = -3(3y + 5) ((30 + 5y) + 3y * (6 + y)) = -3(3y + 5) (30 + 5y + (6 * 3y + y * 3y)) = -3(3y + 5) (30 + 5y + (18y + 3y2)) = -3(3y + 5) Combine like terms: 5y + 18y = 23y (30 + 23y + 3y2) = -3(3y + 5) Reorder the terms: 30 + 23y + 3y2 = -3(5 + 3y) 30 + 23y + 3y2 = (5 * -3 + 3y * -3) 30 + 23y + 3y2 = (-15 + -9y) Solving 30 + 23y + 3y2 = -15 + -9y Solving for variable 'y'. Reorder the terms: 30 + 15 + 23y + 9y + 3y2 = -15 + -9y + 15 + 9y Combine like terms: 30 + 15 = 45 45 + 23y + 9y + 3y2 = -15 + -9y + 15 + 9y Combine like terms: 23y + 9y = 32y 45 + 32y + 3y2 = -15 + -9y + 15 + 9y Reorder the terms: 45 + 32y + 3y2 = -15 + 15 + -9y + 9y Combine like terms: -15 + 15 = 0 45 + 32y + 3y2 = 0 + -9y + 9y 45 + 32y + 3y2 = -9y + 9y Combine like terms: -9y + 9y = 0 45 + 32y + 3y2 = 0 Factor a trinomial. (9 + y)(5 + 3y) = 0Subproblem 1
Set the factor '(9 + y)' equal to zero and attempt to solve: Simplifying 9 + y = 0 Solving 9 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + y = 0 + -9 y = 0 + -9 Combine like terms: 0 + -9 = -9 y = -9 Simplifying y = -9Subproblem 2
Set the factor '(5 + 3y)' equal to zero and attempt to solve: Simplifying 5 + 3y = 0 Solving 5 + 3y = 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 + 3y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3y = 0 + -5 3y = 0 + -5 Combine like terms: 0 + -5 = -5 3y = -5 Divide each side by '3'. y = -1.666666667 Simplifying y = -1.666666667Solution
y = {-9, -1.666666667}
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