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Simplifying (2y + 3)(y + 3) = -2(2y + 3) Reorder the terms: (3 + 2y)(y + 3) = -2(2y + 3) Reorder the terms: (3 + 2y)(3 + y) = -2(2y + 3) Multiply (3 + 2y) * (3 + y) (3(3 + y) + 2y * (3 + y)) = -2(2y + 3) ((3 * 3 + y * 3) + 2y * (3 + y)) = -2(2y + 3) ((9 + 3y) + 2y * (3 + y)) = -2(2y + 3) (9 + 3y + (3 * 2y + y * 2y)) = -2(2y + 3) (9 + 3y + (6y + 2y2)) = -2(2y + 3) Combine like terms: 3y + 6y = 9y (9 + 9y + 2y2) = -2(2y + 3) Reorder the terms: 9 + 9y + 2y2 = -2(3 + 2y) 9 + 9y + 2y2 = (3 * -2 + 2y * -2) 9 + 9y + 2y2 = (-6 + -4y) Solving 9 + 9y + 2y2 = -6 + -4y Solving for variable 'y'. Reorder the terms: 9 + 6 + 9y + 4y + 2y2 = -6 + -4y + 6 + 4y Combine like terms: 9 + 6 = 15 15 + 9y + 4y + 2y2 = -6 + -4y + 6 + 4y Combine like terms: 9y + 4y = 13y 15 + 13y + 2y2 = -6 + -4y + 6 + 4y Reorder the terms: 15 + 13y + 2y2 = -6 + 6 + -4y + 4y Combine like terms: -6 + 6 = 0 15 + 13y + 2y2 = 0 + -4y + 4y 15 + 13y + 2y2 = -4y + 4y Combine like terms: -4y + 4y = 0 15 + 13y + 2y2 = 0 Factor a trinomial. (5 + y)(3 + 2y) = 0Subproblem 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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