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Simplifying (8y + 13)(5y + 24) = 0 Reorder the terms: (13 + 8y)(5y + 24) = 0 Reorder the terms: (13 + 8y)(24 + 5y) = 0 Multiply (13 + 8y) * (24 + 5y) (13(24 + 5y) + 8y * (24 + 5y)) = 0 ((24 * 13 + 5y * 13) + 8y * (24 + 5y)) = 0 ((312 + 65y) + 8y * (24 + 5y)) = 0 (312 + 65y + (24 * 8y + 5y * 8y)) = 0 (312 + 65y + (192y + 40y2)) = 0 Combine like terms: 65y + 192y = 257y (312 + 257y + 40y2) = 0 Solving 312 + 257y + 40y2 = 0 Solving for variable 'y'. Factor a trinomial. (24 + 5y)(13 + 8y) = 0Subproblem 1
Set the factor '(24 + 5y)' equal to zero and attempt to solve: Simplifying 24 + 5y = 0 Solving 24 + 5y = 0 Move all terms containing y to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + 5y = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 5y = 0 + -24 5y = 0 + -24 Combine like terms: 0 + -24 = -24 5y = -24 Divide each side by '5'. y = -4.8 Simplifying y = -4.8Subproblem 2
Set the factor '(13 + 8y)' equal to zero and attempt to solve: Simplifying 13 + 8y = 0 Solving 13 + 8y = 0 Move all terms containing y to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 8y = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 8y = 0 + -13 8y = 0 + -13 Combine like terms: 0 + -13 = -13 8y = -13 Divide each side by '8'. y = -1.625 Simplifying y = -1.625Solution
y = {-4.8, -1.625}
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