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Simplifying (2y + 3)(y + 7) = -2(2y + 3) Reorder the terms: (3 + 2y)(y + 7) = -2(2y + 3) Reorder the terms: (3 + 2y)(7 + y) = -2(2y + 3) Multiply (3 + 2y) * (7 + y) (3(7 + y) + 2y * (7 + y)) = -2(2y + 3) ((7 * 3 + y * 3) + 2y * (7 + y)) = -2(2y + 3) ((21 + 3y) + 2y * (7 + y)) = -2(2y + 3) (21 + 3y + (7 * 2y + y * 2y)) = -2(2y + 3) (21 + 3y + (14y + 2y2)) = -2(2y + 3) Combine like terms: 3y + 14y = 17y (21 + 17y + 2y2) = -2(2y + 3) Reorder the terms: 21 + 17y + 2y2 = -2(3 + 2y) 21 + 17y + 2y2 = (3 * -2 + 2y * -2) 21 + 17y + 2y2 = (-6 + -4y) Solving 21 + 17y + 2y2 = -6 + -4y Solving for variable 'y'. Reorder the terms: 21 + 6 + 17y + 4y + 2y2 = -6 + -4y + 6 + 4y Combine like terms: 21 + 6 = 27 27 + 17y + 4y + 2y2 = -6 + -4y + 6 + 4y Combine like terms: 17y + 4y = 21y 27 + 21y + 2y2 = -6 + -4y + 6 + 4y Reorder the terms: 27 + 21y + 2y2 = -6 + 6 + -4y + 4y Combine like terms: -6 + 6 = 0 27 + 21y + 2y2 = 0 + -4y + 4y 27 + 21y + 2y2 = -4y + 4y Combine like terms: -4y + 4y = 0 27 + 21y + 2y2 = 0 Factor a trinomial. (9 + y)(3 + 2y) = 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 '(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 = {-9, -1.5}
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