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Simplifying (4y + 5)(6 + y) = 0 Reorder the terms: (5 + 4y)(6 + y) = 0 Multiply (5 + 4y) * (6 + y) (5(6 + y) + 4y * (6 + y)) = 0 ((6 * 5 + y * 5) + 4y * (6 + y)) = 0 ((30 + 5y) + 4y * (6 + y)) = 0 (30 + 5y + (6 * 4y + y * 4y)) = 0 (30 + 5y + (24y + 4y2)) = 0 Combine like terms: 5y + 24y = 29y (30 + 29y + 4y2) = 0 Solving 30 + 29y + 4y2 = 0 Solving for variable 'y'. Factor a trinomial. (6 + y)(5 + 4y) = 0Subproblem 1
Set the factor '(6 + y)' equal to zero and attempt to solve: Simplifying 6 + y = 0 Solving 6 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + y = 0 + -6 y = 0 + -6 Combine like terms: 0 + -6 = -6 y = -6 Simplifying y = -6Subproblem 2
Set the factor '(5 + 4y)' equal to zero and attempt to solve: Simplifying 5 + 4y = 0 Solving 5 + 4y = 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 + 4y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4y = 0 + -5 4y = 0 + -5 Combine like terms: 0 + -5 = -5 4y = -5 Divide each side by '4'. y = -1.25 Simplifying y = -1.25Solution
y = {-6, -1.25}
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