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Simplifying (2y + 7)(4 + -1y) = 0 Reorder the terms: (7 + 2y)(4 + -1y) = 0 Multiply (7 + 2y) * (4 + -1y) (7(4 + -1y) + 2y * (4 + -1y)) = 0 ((4 * 7 + -1y * 7) + 2y * (4 + -1y)) = 0 ((28 + -7y) + 2y * (4 + -1y)) = 0 (28 + -7y + (4 * 2y + -1y * 2y)) = 0 (28 + -7y + (8y + -2y2)) = 0 Combine like terms: -7y + 8y = 1y (28 + 1y + -2y2) = 0 Solving 28 + 1y + -2y2 = 0 Solving for variable 'y'. Factor a trinomial. (4 + -1y)(7 + 2y) = 0Subproblem 1
Set the factor '(4 + -1y)' equal to zero and attempt to solve: Simplifying 4 + -1y = 0 Solving 4 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1y = 0 + -4 -1y = 0 + -4 Combine like terms: 0 + -4 = -4 -1y = -4 Divide each side by '-1'. y = 4 Simplifying y = 4Subproblem 2
Set the factor '(7 + 2y)' equal to zero and attempt to solve: Simplifying 7 + 2y = 0 Solving 7 + 2y = 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 + 2y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2y = 0 + -7 2y = 0 + -7 Combine like terms: 0 + -7 = -7 2y = -7 Divide each side by '2'. y = -3.5 Simplifying y = -3.5Solution
y = {4, -3.5}
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