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Simplifying (5y + 7)(y + 5) = 23 Reorder the terms: (7 + 5y)(y + 5) = 23 Reorder the terms: (7 + 5y)(5 + y) = 23 Multiply (7 + 5y) * (5 + y) (7(5 + y) + 5y * (5 + y)) = 23 ((5 * 7 + y * 7) + 5y * (5 + y)) = 23 ((35 + 7y) + 5y * (5 + y)) = 23 (35 + 7y + (5 * 5y + y * 5y)) = 23 (35 + 7y + (25y + 5y2)) = 23 Combine like terms: 7y + 25y = 32y (35 + 32y + 5y2) = 23 Solving 35 + 32y + 5y2 = 23 Solving for variable 'y'. Reorder the terms: 35 + -23 + 32y + 5y2 = 23 + -23 Combine like terms: 35 + -23 = 12 12 + 32y + 5y2 = 23 + -23 Combine like terms: 23 + -23 = 0 12 + 32y + 5y2 = 0 Factor a trinomial. (6 + y)(2 + 5y) = 0Subproblem 1
Set the factor '(6 + y)' equal to zero and attempt to solve: Simplifying 6 + y = 0 Solving 6 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + y = 0 + -6 y = 0 + -6 Combine like terms: 0 + -6 = -6 y = -6 Simplifying y = -6Subproblem 2
Set the factor '(2 + 5y)' equal to zero and attempt to solve: Simplifying 2 + 5y = 0 Solving 2 + 5y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5y = 0 + -2 5y = 0 + -2 Combine like terms: 0 + -2 = -2 5y = -2 Divide each side by '5'. y = -0.4 Simplifying y = -0.4Solution
y = {-6, -0.4}
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