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