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Simplifying (5 + -1y)(2y + 7) = 0 Reorder the terms: (5 + -1y)(7 + 2y) = 0 Multiply (5 + -1y) * (7 + 2y) (5(7 + 2y) + -1y * (7 + 2y)) = 0 ((7 * 5 + 2y * 5) + -1y * (7 + 2y)) = 0 ((35 + 10y) + -1y * (7 + 2y)) = 0 (35 + 10y + (7 * -1y + 2y * -1y)) = 0 (35 + 10y + (-7y + -2y2)) = 0 Combine like terms: 10y + -7y = 3y (35 + 3y + -2y2) = 0 Solving 35 + 3y + -2y2 = 0 Solving for variable 'y'. Factor a trinomial. (5 + -1y)(7 + 2y) = 0Subproblem 1
Set the factor '(5 + -1y)' equal to zero and attempt to solve: Simplifying 5 + -1y = 0 Solving 5 + -1y = 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 + -1y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1y = 0 + -5 -1y = 0 + -5 Combine like terms: 0 + -5 = -5 -1y = -5 Divide each side by '-1'. y = 5 Simplifying y = 5Subproblem 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 = {5, -3.5}
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