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Simplifying (5y + 8)(4 + y) = 0 Reorder the terms: (8 + 5y)(4 + y) = 0 Multiply (8 + 5y) * (4 + y) (8(4 + y) + 5y * (4 + y)) = 0 ((4 * 8 + y * 8) + 5y * (4 + y)) = 0 ((32 + 8y) + 5y * (4 + y)) = 0 (32 + 8y + (4 * 5y + y * 5y)) = 0 (32 + 8y + (20y + 5y2)) = 0 Combine like terms: 8y + 20y = 28y (32 + 28y + 5y2) = 0 Solving 32 + 28y + 5y2 = 0 Solving for variable 'y'. Factor a trinomial. (4 + y)(8 + 5y) = 0Subproblem 1
Set the factor '(4 + y)' equal to zero and attempt to solve: Simplifying 4 + y = 0 Solving 4 + y = 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 + y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + y = 0 + -4 y = 0 + -4 Combine like terms: 0 + -4 = -4 y = -4 Simplifying y = -4Subproblem 2
Set the factor '(8 + 5y)' equal to zero and attempt to solve: Simplifying 8 + 5y = 0 Solving 8 + 5y = 0 Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 5y = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5y = 0 + -8 5y = 0 + -8 Combine like terms: 0 + -8 = -8 5y = -8 Divide each side by '5'. y = -1.6 Simplifying y = -1.6Solution
y = {-4, -1.6}
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