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Simplifying (3y + 5)(2y + 3) = 0 Reorder the terms: (5 + 3y)(2y + 3) = 0 Reorder the terms: (5 + 3y)(3 + 2y) = 0 Multiply (5 + 3y) * (3 + 2y) (5(3 + 2y) + 3y * (3 + 2y)) = 0 ((3 * 5 + 2y * 5) + 3y * (3 + 2y)) = 0 ((15 + 10y) + 3y * (3 + 2y)) = 0 (15 + 10y + (3 * 3y + 2y * 3y)) = 0 (15 + 10y + (9y + 6y2)) = 0 Combine like terms: 10y + 9y = 19y (15 + 19y + 6y2) = 0 Solving 15 + 19y + 6y2 = 0 Solving for variable 'y'. Factor a trinomial. (5 + 3y)(3 + 2y) = 0Subproblem 1
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 = -1.666666667Subproblem 2
Set the factor '(3 + 2y)' equal to zero and attempt to solve: Simplifying 3 + 2y = 0 Solving 3 + 2y = 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 + 2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2y = 0 + -3 2y = 0 + -3 Combine like terms: 0 + -3 = -3 2y = -3 Divide each side by '2'. y = -1.5 Simplifying y = -1.5Solution
y = {-1.666666667, -1.5}
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