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Simplifying (3y + 6)(y + 5) = 0 Reorder the terms: (6 + 3y)(y + 5) = 0 Reorder the terms: (6 + 3y)(5 + y) = 0 Multiply (6 + 3y) * (5 + y) (6(5 + y) + 3y * (5 + y)) = 0 ((5 * 6 + y * 6) + 3y * (5 + y)) = 0 ((30 + 6y) + 3y * (5 + y)) = 0 (30 + 6y + (5 * 3y + y * 3y)) = 0 (30 + 6y + (15y + 3y2)) = 0 Combine like terms: 6y + 15y = 21y (30 + 21y + 3y2) = 0 Solving 30 + 21y + 3y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(10 + 7y + y2) = 0 Factor a trinomial. 3((5 + y)(2 + y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + y)' equal to zero and attempt to solve: Simplifying 5 + y = 0 Solving 5 + y = 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 + y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + y = 0 + -5 y = 0 + -5 Combine like terms: 0 + -5 = -5 y = -5 Simplifying y = -5Subproblem 2
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 = -2Solution
y = {-5, -2}
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