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Simplifying (3y + 1)(2y + 5) = 0 Reorder the terms: (1 + 3y)(2y + 5) = 0 Reorder the terms: (1 + 3y)(5 + 2y) = 0 Multiply (1 + 3y) * (5 + 2y) (1(5 + 2y) + 3y * (5 + 2y)) = 0 ((5 * 1 + 2y * 1) + 3y * (5 + 2y)) = 0 ((5 + 2y) + 3y * (5 + 2y)) = 0 (5 + 2y + (5 * 3y + 2y * 3y)) = 0 (5 + 2y + (15y + 6y2)) = 0 Combine like terms: 2y + 15y = 17y (5 + 17y + 6y2) = 0 Solving 5 + 17y + 6y2 = 0 Solving for variable 'y'. Factor a trinomial. (5 + 2y)(1 + 3y) = 0Subproblem 1
Set the factor '(5 + 2y)' equal to zero and attempt to solve: Simplifying 5 + 2y = 0 Solving 5 + 2y = 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 + 2y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2y = 0 + -5 2y = 0 + -5 Combine like terms: 0 + -5 = -5 2y = -5 Divide each side by '2'. y = -2.5 Simplifying y = -2.5Subproblem 2
Set the factor '(1 + 3y)' equal to zero and attempt to solve: Simplifying 1 + 3y = 0 Solving 1 + 3y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3y = 0 + -1 3y = 0 + -1 Combine like terms: 0 + -1 = -1 3y = -1 Divide each side by '3'. y = -0.3333333333 Simplifying y = -0.3333333333Solution
y = {-2.5, -0.3333333333}
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