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Simplifying (3y + 5)(2 + y) = 0 Reorder the terms: (5 + 3y)(2 + y) = 0 Multiply (5 + 3y) * (2 + y) (5(2 + y) + 3y * (2 + y)) = 0 ((2 * 5 + y * 5) + 3y * (2 + y)) = 0 ((10 + 5y) + 3y * (2 + y)) = 0 (10 + 5y + (2 * 3y + y * 3y)) = 0 (10 + 5y + (6y + 3y2)) = 0 Combine like terms: 5y + 6y = 11y (10 + 11y + 3y2) = 0 Solving 10 + 11y + 3y2 = 0 Solving for variable 'y'. Factor a trinomial. (2 + y)(5 + 3y) = 0Subproblem 1
Set the factor '(2 + y)' equal to zero and attempt to solve: Simplifying 2 + y = 0 Solving 2 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + y = 0 + -2 y = 0 + -2 Combine like terms: 0 + -2 = -2 y = -2 Simplifying y = -2Subproblem 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 = {-2, -1.666666667}
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