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Simplifying (3y + 2)(9 + y) = 0 Reorder the terms: (2 + 3y)(9 + y) = 0 Multiply (2 + 3y) * (9 + y) (2(9 + y) + 3y * (9 + y)) = 0 ((9 * 2 + y * 2) + 3y * (9 + y)) = 0 ((18 + 2y) + 3y * (9 + y)) = 0 (18 + 2y + (9 * 3y + y * 3y)) = 0 (18 + 2y + (27y + 3y2)) = 0 Combine like terms: 2y + 27y = 29y (18 + 29y + 3y2) = 0 Solving 18 + 29y + 3y2 = 0 Solving for variable 'y'. Factor a trinomial. (9 + y)(2 + 3y) = 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 '(2 + 3y)' equal to zero and attempt to solve: Simplifying 2 + 3y = 0 Solving 2 + 3y = 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 + 3y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3y = 0 + -2 3y = 0 + -2 Combine like terms: 0 + -2 = -2 3y = -2 Divide each side by '3'. y = -0.6666666667 Simplifying y = -0.6666666667Solution
y = {-9, -0.6666666667}
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