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Simplifying (2y + 7)(5 + y) = 0 Reorder the terms: (7 + 2y)(5 + y) = 0 Multiply (7 + 2y) * (5 + y) (7(5 + y) + 2y * (5 + y)) = 0 ((5 * 7 + y * 7) + 2y * (5 + y)) = 0 ((35 + 7y) + 2y * (5 + y)) = 0 (35 + 7y + (5 * 2y + y * 2y)) = 0 (35 + 7y + (10y + 2y2)) = 0 Combine like terms: 7y + 10y = 17y (35 + 17y + 2y2) = 0 Solving 35 + 17y + 2y2 = 0 Solving for variable 'y'. Factor a trinomial. (5 + y)(7 + 2y) = 0Subproblem 1
Set the factor '(5 + y)' equal to zero and attempt to solve: Simplifying 5 + y = 0 Solving 5 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + y = 0 + -5 y = 0 + -5 Combine like terms: 0 + -5 = -5 y = -5 Simplifying y = -5Subproblem 2
Set the factor '(7 + 2y)' equal to zero and attempt to solve: Simplifying 7 + 2y = 0 Solving 7 + 2y = 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 + 2y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2y = 0 + -7 2y = 0 + -7 Combine like terms: 0 + -7 = -7 2y = -7 Divide each side by '2'. y = -3.5 Simplifying y = -3.5Solution
y = {-5, -3.5}
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