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