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Simplifying (7 + y)(3y + 5) = 0 Reorder the terms: (7 + y)(5 + 3y) = 0 Multiply (7 + y) * (5 + 3y) (7(5 + 3y) + y(5 + 3y)) = 0 ((5 * 7 + 3y * 7) + y(5 + 3y)) = 0 ((35 + 21y) + y(5 + 3y)) = 0 (35 + 21y + (5 * y + 3y * y)) = 0 (35 + 21y + (5y + 3y2)) = 0 Combine like terms: 21y + 5y = 26y (35 + 26y + 3y2) = 0 Solving 35 + 26y + 3y2 = 0 Solving for variable 'y'. Factor a trinomial. (7 + y)(5 + 3y) = 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 '(5 + 3y)' equal to zero and attempt to solve: Simplifying 5 + 3y = 0 Solving 5 + 3y = 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 + 3y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3y = 0 + -5 3y = 0 + -5 Combine like terms: 0 + -5 = -5 3y = -5 Divide each side by '3'. y = -1.666666667 Simplifying y = -1.666666667Solution
y = {-7, -1.666666667}
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