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Simplifying 6(2y + 5)(2y + 5) = 11(2y + 5) + 10 Reorder the terms: 6(5 + 2y)(2y + 5) = 11(2y + 5) + 10 Reorder the terms: 6(5 + 2y)(5 + 2y) = 11(2y + 5) + 10 Multiply (5 + 2y) * (5 + 2y) 6(5(5 + 2y) + 2y * (5 + 2y)) = 11(2y + 5) + 10 6((5 * 5 + 2y * 5) + 2y * (5 + 2y)) = 11(2y + 5) + 10 6((25 + 10y) + 2y * (5 + 2y)) = 11(2y + 5) + 10 6(25 + 10y + (5 * 2y + 2y * 2y)) = 11(2y + 5) + 10 6(25 + 10y + (10y + 4y2)) = 11(2y + 5) + 10 Combine like terms: 10y + 10y = 20y 6(25 + 20y + 4y2) = 11(2y + 5) + 10 (25 * 6 + 20y * 6 + 4y2 * 6) = 11(2y + 5) + 10 (150 + 120y + 24y2) = 11(2y + 5) + 10 Reorder the terms: 150 + 120y + 24y2 = 11(5 + 2y) + 10 150 + 120y + 24y2 = (5 * 11 + 2y * 11) + 10 150 + 120y + 24y2 = (55 + 22y) + 10 Reorder the terms: 150 + 120y + 24y2 = 55 + 10 + 22y Combine like terms: 55 + 10 = 65 150 + 120y + 24y2 = 65 + 22y Solving 150 + 120y + 24y2 = 65 + 22y Solving for variable 'y'. Reorder the terms: 150 + -65 + 120y + -22y + 24y2 = 65 + 22y + -65 + -22y Combine like terms: 150 + -65 = 85 85 + 120y + -22y + 24y2 = 65 + 22y + -65 + -22y Combine like terms: 120y + -22y = 98y 85 + 98y + 24y2 = 65 + 22y + -65 + -22y Reorder the terms: 85 + 98y + 24y2 = 65 + -65 + 22y + -22y Combine like terms: 65 + -65 = 0 85 + 98y + 24y2 = 0 + 22y + -22y 85 + 98y + 24y2 = 22y + -22y Combine like terms: 22y + -22y = 0 85 + 98y + 24y2 = 0 Factor a trinomial. (17 + 6y)(5 + 4y) = 0Subproblem 1
Set the factor '(17 + 6y)' equal to zero and attempt to solve: Simplifying 17 + 6y = 0 Solving 17 + 6y = 0 Move all terms containing y to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 6y = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 6y = 0 + -17 6y = 0 + -17 Combine like terms: 0 + -17 = -17 6y = -17 Divide each side by '6'. y = -2.833333333 Simplifying y = -2.833333333Subproblem 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 = {-2.833333333, -1.25}
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