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Simplifying (4y + 9)(3 + y) = 0 Reorder the terms: (9 + 4y)(3 + y) = 0 Multiply (9 + 4y) * (3 + y) (9(3 + y) + 4y * (3 + y)) = 0 ((3 * 9 + y * 9) + 4y * (3 + y)) = 0 ((27 + 9y) + 4y * (3 + y)) = 0 (27 + 9y + (3 * 4y + y * 4y)) = 0 (27 + 9y + (12y + 4y2)) = 0 Combine like terms: 9y + 12y = 21y (27 + 21y + 4y2) = 0 Solving 27 + 21y + 4y2 = 0 Solving for variable 'y'. Factor a trinomial. (3 + y)(9 + 4y) = 0Subproblem 1
Set the factor '(3 + y)' equal to zero and attempt to solve: Simplifying 3 + y = 0 Solving 3 + y = 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 + y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + y = 0 + -3 y = 0 + -3 Combine like terms: 0 + -3 = -3 y = -3 Simplifying y = -3Subproblem 2
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 = -2.25Solution
y = {-3, -2.25}
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