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Simplifying (9 + y)(2y + 5) = 0 Reorder the terms: (9 + y)(5 + 2y) = 0 Multiply (9 + y) * (5 + 2y) (9(5 + 2y) + y(5 + 2y)) = 0 ((5 * 9 + 2y * 9) + y(5 + 2y)) = 0 ((45 + 18y) + y(5 + 2y)) = 0 (45 + 18y + (5 * y + 2y * y)) = 0 (45 + 18y + (5y + 2y2)) = 0 Combine like terms: 18y + 5y = 23y (45 + 23y + 2y2) = 0 Solving 45 + 23y + 2y2 = 0 Solving for variable 'y'. Factor a trinomial. (9 + y)(5 + 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 '(5 + 2y)' equal to zero and attempt to solve: Simplifying 5 + 2y = 0 Solving 5 + 2y = 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 + 2y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2y = 0 + -5 2y = 0 + -5 Combine like terms: 0 + -5 = -5 2y = -5 Divide each side by '2'. y = -2.5 Simplifying y = -2.5Solution
y = {-9, -2.5}
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