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Simplifying (y + 4)(2y + 3) = 7 Reorder the terms: (4 + y)(2y + 3) = 7 Reorder the terms: (4 + y)(3 + 2y) = 7 Multiply (4 + y) * (3 + 2y) (4(3 + 2y) + y(3 + 2y)) = 7 ((3 * 4 + 2y * 4) + y(3 + 2y)) = 7 ((12 + 8y) + y(3 + 2y)) = 7 (12 + 8y + (3 * y + 2y * y)) = 7 (12 + 8y + (3y + 2y2)) = 7 Combine like terms: 8y + 3y = 11y (12 + 11y + 2y2) = 7 Solving 12 + 11y + 2y2 = 7 Solving for variable 'y'. Reorder the terms: 12 + -7 + 11y + 2y2 = 7 + -7 Combine like terms: 12 + -7 = 5 5 + 11y + 2y2 = 7 + -7 Combine like terms: 7 + -7 = 0 5 + 11y + 2y2 = 0 Factor a trinomial. (5 + y)(1 + 2y) = 0Subproblem 1
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 = -5Subproblem 2
Set the factor '(1 + 2y)' equal to zero and attempt to solve: Simplifying 1 + 2y = 0 Solving 1 + 2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2y = 0 + -1 2y = 0 + -1 Combine like terms: 0 + -1 = -1 2y = -1 Divide each side by '2'. y = -0.5 Simplifying y = -0.5Solution
y = {-5, -0.5}
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