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Simplifying (y + 7)(y + 5) = 0 Reorder the terms: (7 + y)(y + 5) = 0 Reorder the terms: (7 + y)(5 + y) = 0 Multiply (7 + y) * (5 + y) (7(5 + y) + y(5 + y)) = 0 ((5 * 7 + y * 7) + y(5 + y)) = 0 ((35 + 7y) + y(5 + y)) = 0 (35 + 7y + (5 * y + y * y)) = 0 (35 + 7y + (5y + y2)) = 0 Combine like terms: 7y + 5y = 12y (35 + 12y + y2) = 0 Solving 35 + 12y + y2 = 0 Solving for variable 'y'. Factor a trinomial. (7 + y)(5 + y) = 0Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve: Simplifying 7 + y = 0 Solving 7 + y = 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 + y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + y = 0 + -7 y = 0 + -7 Combine like terms: 0 + -7 = -7 y = -7 Simplifying y = -7Subproblem 2
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 = -5Solution
y = {-7, -5}
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