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Simplifying (3y + 7)(9 + y) = 0 Reorder the terms: (7 + 3y)(9 + y) = 0 Multiply (7 + 3y) * (9 + y) (7(9 + y) + 3y * (9 + y)) = 0 ((9 * 7 + y * 7) + 3y * (9 + y)) = 0 ((63 + 7y) + 3y * (9 + y)) = 0 (63 + 7y + (9 * 3y + y * 3y)) = 0 (63 + 7y + (27y + 3y2)) = 0 Combine like terms: 7y + 27y = 34y (63 + 34y + 3y2) = 0 Solving 63 + 34y + 3y2 = 0 Solving for variable 'y'. Factor a trinomial. (9 + y)(7 + 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 '(7 + 3y)' equal to zero and attempt to solve: Simplifying 7 + 3y = 0 Solving 7 + 3y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3y = 0 + -7 3y = 0 + -7 Combine like terms: 0 + -7 = -7 3y = -7 Divide each side by '3'. y = -2.333333333 Simplifying y = -2.333333333Solution
y = {-9, -2.333333333}
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