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Simplifying (7a + 8)(12a + 3) + (11a + 15)(7a + 8) = 0 Reorder the terms: (8 + 7a)(12a + 3) + (11a + 15)(7a + 8) = 0 Reorder the terms: (8 + 7a)(3 + 12a) + (11a + 15)(7a + 8) = 0 Multiply (8 + 7a) * (3 + 12a) (8(3 + 12a) + 7a * (3 + 12a)) + (11a + 15)(7a + 8) = 0 ((3 * 8 + 12a * 8) + 7a * (3 + 12a)) + (11a + 15)(7a + 8) = 0 ((24 + 96a) + 7a * (3 + 12a)) + (11a + 15)(7a + 8) = 0 (24 + 96a + (3 * 7a + 12a * 7a)) + (11a + 15)(7a + 8) = 0 (24 + 96a + (21a + 84a2)) + (11a + 15)(7a + 8) = 0 Combine like terms: 96a + 21a = 117a (24 + 117a + 84a2) + (11a + 15)(7a + 8) = 0 Reorder the terms: 24 + 117a + 84a2 + (15 + 11a)(7a + 8) = 0 Reorder the terms: 24 + 117a + 84a2 + (15 + 11a)(8 + 7a) = 0 Multiply (15 + 11a) * (8 + 7a) 24 + 117a + 84a2 + (15(8 + 7a) + 11a * (8 + 7a)) = 0 24 + 117a + 84a2 + ((8 * 15 + 7a * 15) + 11a * (8 + 7a)) = 0 24 + 117a + 84a2 + ((120 + 105a) + 11a * (8 + 7a)) = 0 24 + 117a + 84a2 + (120 + 105a + (8 * 11a + 7a * 11a)) = 0 24 + 117a + 84a2 + (120 + 105a + (88a + 77a2)) = 0 Combine like terms: 105a + 88a = 193a 24 + 117a + 84a2 + (120 + 193a + 77a2) = 0 Reorder the terms: 24 + 120 + 117a + 193a + 84a2 + 77a2 = 0 Combine like terms: 24 + 120 = 144 144 + 117a + 193a + 84a2 + 77a2 = 0 Combine like terms: 117a + 193a = 310a 144 + 310a + 84a2 + 77a2 = 0 Combine like terms: 84a2 + 77a2 = 161a2 144 + 310a + 161a2 = 0 Solving 144 + 310a + 161a2 = 0 Solving for variable 'a'. Factor a trinomial. (8 + 7a)(18 + 23a) = 0Subproblem 1
Set the factor '(8 + 7a)' equal to zero and attempt to solve: Simplifying 8 + 7a = 0 Solving 8 + 7a = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 7a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 7a = 0 + -8 7a = 0 + -8 Combine like terms: 0 + -8 = -8 7a = -8 Divide each side by '7'. a = -1.142857143 Simplifying a = -1.142857143Subproblem 2
Set the factor '(18 + 23a)' equal to zero and attempt to solve: Simplifying 18 + 23a = 0 Solving 18 + 23a = 0 Move all terms containing a to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + 23a = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 23a = 0 + -18 23a = 0 + -18 Combine like terms: 0 + -18 = -18 23a = -18 Divide each side by '23'. a = -0.7826086957 Simplifying a = -0.7826086957Solution
a = {-1.142857143, -0.7826086957}
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