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Simplifying (3a + 13)(9a + 15) + -1(11a + 7)(3a + 13) = 0 Reorder the terms: (13 + 3a)(9a + 15) + -1(11a + 7)(3a + 13) = 0 Reorder the terms: (13 + 3a)(15 + 9a) + -1(11a + 7)(3a + 13) = 0 Multiply (13 + 3a) * (15 + 9a) (13(15 + 9a) + 3a * (15 + 9a)) + -1(11a + 7)(3a + 13) = 0 ((15 * 13 + 9a * 13) + 3a * (15 + 9a)) + -1(11a + 7)(3a + 13) = 0 ((195 + 117a) + 3a * (15 + 9a)) + -1(11a + 7)(3a + 13) = 0 (195 + 117a + (15 * 3a + 9a * 3a)) + -1(11a + 7)(3a + 13) = 0 (195 + 117a + (45a + 27a2)) + -1(11a + 7)(3a + 13) = 0 Combine like terms: 117a + 45a = 162a (195 + 162a + 27a2) + -1(11a + 7)(3a + 13) = 0 Reorder the terms: 195 + 162a + 27a2 + -1(7 + 11a)(3a + 13) = 0 Reorder the terms: 195 + 162a + 27a2 + -1(7 + 11a)(13 + 3a) = 0 Multiply (7 + 11a) * (13 + 3a) 195 + 162a + 27a2 + -1(7(13 + 3a) + 11a * (13 + 3a)) = 0 195 + 162a + 27a2 + -1((13 * 7 + 3a * 7) + 11a * (13 + 3a)) = 0 195 + 162a + 27a2 + -1((91 + 21a) + 11a * (13 + 3a)) = 0 195 + 162a + 27a2 + -1(91 + 21a + (13 * 11a + 3a * 11a)) = 0 195 + 162a + 27a2 + -1(91 + 21a + (143a + 33a2)) = 0 Combine like terms: 21a + 143a = 164a 195 + 162a + 27a2 + -1(91 + 164a + 33a2) = 0 195 + 162a + 27a2 + (91 * -1 + 164a * -1 + 33a2 * -1) = 0 195 + 162a + 27a2 + (-91 + -164a + -33a2) = 0 Reorder the terms: 195 + -91 + 162a + -164a + 27a2 + -33a2 = 0 Combine like terms: 195 + -91 = 104 104 + 162a + -164a + 27a2 + -33a2 = 0 Combine like terms: 162a + -164a = -2a 104 + -2a + 27a2 + -33a2 = 0 Combine like terms: 27a2 + -33a2 = -6a2 104 + -2a + -6a2 = 0 Solving 104 + -2a + -6a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(52 + -1a + -3a2) = 0 Factor a trinomial. 2((4 + -1a)(13 + 3a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -1a)' equal to zero and attempt to solve: Simplifying 4 + -1a = 0 Solving 4 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1a = 0 + -4 -1a = 0 + -4 Combine like terms: 0 + -4 = -4 -1a = -4 Divide each side by '-1'. a = 4 Simplifying a = 4Subproblem 2
Set the factor '(13 + 3a)' equal to zero and attempt to solve: Simplifying 13 + 3a = 0 Solving 13 + 3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 3a = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 3a = 0 + -13 3a = 0 + -13 Combine like terms: 0 + -13 = -13 3a = -13 Divide each side by '3'. a = -4.333333333 Simplifying a = -4.333333333Solution
a = {4, -4.333333333}
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