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Simplifying (2y + 1)(7 + y) = 0 Reorder the terms: (1 + 2y)(7 + y) = 0 Multiply (1 + 2y) * (7 + y) (1(7 + y) + 2y * (7 + y)) = 0 ((7 * 1 + y * 1) + 2y * (7 + y)) = 0 ((7 + 1y) + 2y * (7 + y)) = 0 (7 + 1y + (7 * 2y + y * 2y)) = 0 (7 + 1y + (14y + 2y2)) = 0 Combine like terms: 1y + 14y = 15y (7 + 15y + 2y2) = 0 Solving 7 + 15y + 2y2 = 0 Solving for variable 'y'. Factor a trinomial. (7 + y)(1 + 2y) = 0Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve: Simplifying 7 + y = 0 Solving 7 + y = 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 + y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + y = 0 + -7 y = 0 + -7 Combine like terms: 0 + -7 = -7 y = -7 Simplifying y = -7Subproblem 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 = {-7, -0.5}
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