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Simplifying (3 + y)(5y + 7) = 0 Reorder the terms: (3 + y)(7 + 5y) = 0 Multiply (3 + y) * (7 + 5y) (3(7 + 5y) + y(7 + 5y)) = 0 ((7 * 3 + 5y * 3) + y(7 + 5y)) = 0 ((21 + 15y) + y(7 + 5y)) = 0 (21 + 15y + (7 * y + 5y * y)) = 0 (21 + 15y + (7y + 5y2)) = 0 Combine like terms: 15y + 7y = 22y (21 + 22y + 5y2) = 0 Solving 21 + 22y + 5y2 = 0 Solving for variable 'y'. Factor a trinomial. (3 + y)(7 + 5y) = 0Subproblem 1
Set the factor '(3 + y)' equal to zero and attempt to solve: Simplifying 3 + y = 0 Solving 3 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + y = 0 + -3 y = 0 + -3 Combine like terms: 0 + -3 = -3 y = -3 Simplifying y = -3Subproblem 2
Set the factor '(7 + 5y)' equal to zero and attempt to solve: Simplifying 7 + 5y = 0 Solving 7 + 5y = 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 + 5y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5y = 0 + -7 5y = 0 + -7 Combine like terms: 0 + -7 = -7 5y = -7 Divide each side by '5'. y = -1.4 Simplifying y = -1.4Solution
y = {-3, -1.4}
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