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Simplifying (2y + 3)(y + 3) = -4(2y + 3) Reorder the terms: (3 + 2y)(y + 3) = -4(2y + 3) Reorder the terms: (3 + 2y)(3 + y) = -4(2y + 3) Multiply (3 + 2y) * (3 + y) (3(3 + y) + 2y * (3 + y)) = -4(2y + 3) ((3 * 3 + y * 3) + 2y * (3 + y)) = -4(2y + 3) ((9 + 3y) + 2y * (3 + y)) = -4(2y + 3) (9 + 3y + (3 * 2y + y * 2y)) = -4(2y + 3) (9 + 3y + (6y + 2y2)) = -4(2y + 3) Combine like terms: 3y + 6y = 9y (9 + 9y + 2y2) = -4(2y + 3) Reorder the terms: 9 + 9y + 2y2 = -4(3 + 2y) 9 + 9y + 2y2 = (3 * -4 + 2y * -4) 9 + 9y + 2y2 = (-12 + -8y) Solving 9 + 9y + 2y2 = -12 + -8y Solving for variable 'y'. Reorder the terms: 9 + 12 + 9y + 8y + 2y2 = -12 + -8y + 12 + 8y Combine like terms: 9 + 12 = 21 21 + 9y + 8y + 2y2 = -12 + -8y + 12 + 8y Combine like terms: 9y + 8y = 17y 21 + 17y + 2y2 = -12 + -8y + 12 + 8y Reorder the terms: 21 + 17y + 2y2 = -12 + 12 + -8y + 8y Combine like terms: -12 + 12 = 0 21 + 17y + 2y2 = 0 + -8y + 8y 21 + 17y + 2y2 = -8y + 8y Combine like terms: -8y + 8y = 0 21 + 17y + 2y2 = 0 Factor a trinomial. (7 + y)(3 + 2y) = 0Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve: Simplifying 7 + y = 0 Solving 7 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + y = 0 + -7 y = 0 + -7 Combine like terms: 0 + -7 = -7 y = -7 Simplifying y = -7Subproblem 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 = {-7, -1.5}
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