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Simplifying (5 + y)(2y + 9) = 0 Reorder the terms: (5 + y)(9 + 2y) = 0 Multiply (5 + y) * (9 + 2y) (5(9 + 2y) + y(9 + 2y)) = 0 ((9 * 5 + 2y * 5) + y(9 + 2y)) = 0 ((45 + 10y) + y(9 + 2y)) = 0 (45 + 10y + (9 * y + 2y * y)) = 0 (45 + 10y + (9y + 2y2)) = 0 Combine like terms: 10y + 9y = 19y (45 + 19y + 2y2) = 0 Solving 45 + 19y + 2y2 = 0 Solving for variable 'y'. Factor a trinomial. (5 + y)(9 + 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 '(9 + 2y)' equal to zero and attempt to solve: Simplifying 9 + 2y = 0 Solving 9 + 2y = 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 + 2y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2y = 0 + -9 2y = 0 + -9 Combine like terms: 0 + -9 = -9 2y = -9 Divide each side by '2'. y = -4.5 Simplifying y = -4.5Solution
y = {-5, -4.5}
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