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Simplifying (3y + 4)(5 + y) = 0 Reorder the terms: (4 + 3y)(5 + y) = 0 Multiply (4 + 3y) * (5 + y) (4(5 + y) + 3y * (5 + y)) = 0 ((5 * 4 + y * 4) + 3y * (5 + y)) = 0 ((20 + 4y) + 3y * (5 + y)) = 0 (20 + 4y + (5 * 3y + y * 3y)) = 0 (20 + 4y + (15y + 3y2)) = 0 Combine like terms: 4y + 15y = 19y (20 + 19y + 3y2) = 0 Solving 20 + 19y + 3y2 = 0 Solving for variable 'y'. Factor a trinomial. (5 + y)(4 + 3y) = 0Subproblem 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 '(4 + 3y)' equal to zero and attempt to solve: Simplifying 4 + 3y = 0 Solving 4 + 3y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3y = 0 + -4 3y = 0 + -4 Combine like terms: 0 + -4 = -4 3y = -4 Divide each side by '3'. y = -1.333333333 Simplifying y = -1.333333333Solution
y = {-5, -1.333333333}
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