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Simplifying (10y + 4)(13y + 5) + (7y + 8)(10y + 4) = 0 Reorder the terms: (4 + 10y)(13y + 5) + (7y + 8)(10y + 4) = 0 Reorder the terms: (4 + 10y)(5 + 13y) + (7y + 8)(10y + 4) = 0 Multiply (4 + 10y) * (5 + 13y) (4(5 + 13y) + 10y * (5 + 13y)) + (7y + 8)(10y + 4) = 0 ((5 * 4 + 13y * 4) + 10y * (5 + 13y)) + (7y + 8)(10y + 4) = 0 ((20 + 52y) + 10y * (5 + 13y)) + (7y + 8)(10y + 4) = 0 (20 + 52y + (5 * 10y + 13y * 10y)) + (7y + 8)(10y + 4) = 0 (20 + 52y + (50y + 130y2)) + (7y + 8)(10y + 4) = 0 Combine like terms: 52y + 50y = 102y (20 + 102y + 130y2) + (7y + 8)(10y + 4) = 0 Reorder the terms: 20 + 102y + 130y2 + (8 + 7y)(10y + 4) = 0 Reorder the terms: 20 + 102y + 130y2 + (8 + 7y)(4 + 10y) = 0 Multiply (8 + 7y) * (4 + 10y) 20 + 102y + 130y2 + (8(4 + 10y) + 7y * (4 + 10y)) = 0 20 + 102y + 130y2 + ((4 * 8 + 10y * 8) + 7y * (4 + 10y)) = 0 20 + 102y + 130y2 + ((32 + 80y) + 7y * (4 + 10y)) = 0 20 + 102y + 130y2 + (32 + 80y + (4 * 7y + 10y * 7y)) = 0 20 + 102y + 130y2 + (32 + 80y + (28y + 70y2)) = 0 Combine like terms: 80y + 28y = 108y 20 + 102y + 130y2 + (32 + 108y + 70y2) = 0 Reorder the terms: 20 + 32 + 102y + 108y + 130y2 + 70y2 = 0 Combine like terms: 20 + 32 = 52 52 + 102y + 108y + 130y2 + 70y2 = 0 Combine like terms: 102y + 108y = 210y 52 + 210y + 130y2 + 70y2 = 0 Combine like terms: 130y2 + 70y2 = 200y2 52 + 210y + 200y2 = 0 Solving 52 + 210y + 200y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(26 + 105y + 100y2) = 0 Factor a trinomial. 2((13 + 20y)(2 + 5y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + 20y)' equal to zero and attempt to solve: Simplifying 13 + 20y = 0 Solving 13 + 20y = 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 + 20y = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 20y = 0 + -13 20y = 0 + -13 Combine like terms: 0 + -13 = -13 20y = -13 Divide each side by '20'. y = -0.65 Simplifying y = -0.65Subproblem 2
Set the factor '(2 + 5y)' equal to zero and attempt to solve: Simplifying 2 + 5y = 0 Solving 2 + 5y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5y = 0 + -2 5y = 0 + -2 Combine like terms: 0 + -2 = -2 5y = -2 Divide each side by '5'. y = -0.4 Simplifying y = -0.4Solution
y = {-0.65, -0.4}
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