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Simplifying (4y + 9)(2 + y) = 0 Reorder the terms: (9 + 4y)(2 + y) = 0 Multiply (9 + 4y) * (2 + y) (9(2 + y) + 4y * (2 + y)) = 0 ((2 * 9 + y * 9) + 4y * (2 + y)) = 0 ((18 + 9y) + 4y * (2 + y)) = 0 (18 + 9y + (2 * 4y + y * 4y)) = 0 (18 + 9y + (8y + 4y2)) = 0 Combine like terms: 9y + 8y = 17y (18 + 17y + 4y2) = 0 Solving 18 + 17y + 4y2 = 0 Solving for variable 'y'. Factor a trinomial. (9 + 4y)(2 + y) = 0Subproblem 1
Set the factor '(9 + 4y)' equal to zero and attempt to solve: Simplifying 9 + 4y = 0 Solving 9 + 4y = 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 + 4y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4y = 0 + -9 4y = 0 + -9 Combine like terms: 0 + -9 = -9 4y = -9 Divide each side by '4'. y = -2.25 Simplifying y = -2.25Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve: Simplifying 2 + y = 0 Solving 2 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + y = 0 + -2 y = 0 + -2 Combine like terms: 0 + -2 = -2 y = -2 Simplifying y = -2Solution
y = {-2.25, -2}
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