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Simplifying (5y + 8)(8y + 3) = 0 Reorder the terms: (8 + 5y)(8y + 3) = 0 Reorder the terms: (8 + 5y)(3 + 8y) = 0 Multiply (8 + 5y) * (3 + 8y) (8(3 + 8y) + 5y * (3 + 8y)) = 0 ((3 * 8 + 8y * 8) + 5y * (3 + 8y)) = 0 ((24 + 64y) + 5y * (3 + 8y)) = 0 (24 + 64y + (3 * 5y + 8y * 5y)) = 0 (24 + 64y + (15y + 40y2)) = 0 Combine like terms: 64y + 15y = 79y (24 + 79y + 40y2) = 0 Solving 24 + 79y + 40y2 = 0 Solving for variable 'y'. Factor a trinomial. (8 + 5y)(3 + 8y) = 0Subproblem 1
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 = -1.6Subproblem 2
Set the factor '(3 + 8y)' equal to zero and attempt to solve: Simplifying 3 + 8y = 0 Solving 3 + 8y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 8y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8y = 0 + -3 8y = 0 + -3 Combine like terms: 0 + -3 = -3 8y = -3 Divide each side by '8'. y = -0.375 Simplifying y = -0.375Solution
y = {-1.6, -0.375}
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