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Simplifying (2y + 1)(9 + y) = 0 Reorder the terms: (1 + 2y)(9 + y) = 0 Multiply (1 + 2y) * (9 + y) (1(9 + y) + 2y * (9 + y)) = 0 ((9 * 1 + y * 1) + 2y * (9 + y)) = 0 ((9 + 1y) + 2y * (9 + y)) = 0 (9 + 1y + (9 * 2y + y * 2y)) = 0 (9 + 1y + (18y + 2y2)) = 0 Combine like terms: 1y + 18y = 19y (9 + 19y + 2y2) = 0 Solving 9 + 19y + 2y2 = 0 Solving for variable 'y'. Factor a trinomial. (9 + y)(1 + 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 '(1 + 2y)' equal to zero and attempt to solve: Simplifying 1 + 2y = 0 Solving 1 + 2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2y = 0 + -1 2y = 0 + -1 Combine like terms: 0 + -1 = -1 2y = -1 Divide each side by '2'. y = -0.5 Simplifying y = -0.5Solution
y = {-9, -0.5}
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