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Simplifying (7y + 9)(y + 7) = 47 Reorder the terms: (9 + 7y)(y + 7) = 47 Reorder the terms: (9 + 7y)(7 + y) = 47 Multiply (9 + 7y) * (7 + y) (9(7 + y) + 7y * (7 + y)) = 47 ((7 * 9 + y * 9) + 7y * (7 + y)) = 47 ((63 + 9y) + 7y * (7 + y)) = 47 (63 + 9y + (7 * 7y + y * 7y)) = 47 (63 + 9y + (49y + 7y2)) = 47 Combine like terms: 9y + 49y = 58y (63 + 58y + 7y2) = 47 Solving 63 + 58y + 7y2 = 47 Solving for variable 'y'. Reorder the terms: 63 + -47 + 58y + 7y2 = 47 + -47 Combine like terms: 63 + -47 = 16 16 + 58y + 7y2 = 47 + -47 Combine like terms: 47 + -47 = 0 16 + 58y + 7y2 = 0 Factor a trinomial. (8 + y)(2 + 7y) = 0Subproblem 1
Set the factor '(8 + y)' equal to zero and attempt to solve: Simplifying 8 + y = 0 Solving 8 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + y = 0 + -8 Combine like terms: 8 + -8 = 0 0 + y = 0 + -8 y = 0 + -8 Combine like terms: 0 + -8 = -8 y = -8 Simplifying y = -8Subproblem 2
Set the factor '(2 + 7y)' equal to zero and attempt to solve: Simplifying 2 + 7y = 0 Solving 2 + 7y = 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 + 7y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7y = 0 + -2 7y = 0 + -2 Combine like terms: 0 + -2 = -2 7y = -2 Divide each side by '7'. y = -0.2857142857 Simplifying y = -0.2857142857Solution
y = {-8, -0.2857142857}
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