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Simplifying (6a + 3)(5a + 8) = 0 Reorder the terms: (3 + 6a)(5a + 8) = 0 Reorder the terms: (3 + 6a)(8 + 5a) = 0 Multiply (3 + 6a) * (8 + 5a) (3(8 + 5a) + 6a * (8 + 5a)) = 0 ((8 * 3 + 5a * 3) + 6a * (8 + 5a)) = 0 ((24 + 15a) + 6a * (8 + 5a)) = 0 (24 + 15a + (8 * 6a + 5a * 6a)) = 0 (24 + 15a + (48a + 30a2)) = 0 Combine like terms: 15a + 48a = 63a (24 + 63a + 30a2) = 0 Solving 24 + 63a + 30a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(8 + 21a + 10a2) = 0 Factor a trinomial. 3((8 + 5a)(1 + 2a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + 5a)' equal to zero and attempt to solve: Simplifying 8 + 5a = 0 Solving 8 + 5a = 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 + 5a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5a = 0 + -8 5a = 0 + -8 Combine like terms: 0 + -8 = -8 5a = -8 Divide each side by '5'. a = -1.6 Simplifying a = -1.6Subproblem 2
Set the factor '(1 + 2a)' equal to zero and attempt to solve: Simplifying 1 + 2a = 0 Solving 1 + 2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2a = 0 + -1 2a = 0 + -1 Combine like terms: 0 + -1 = -1 2a = -1 Divide each side by '2'. a = -0.5 Simplifying a = -0.5Solution
a = {-1.6, -0.5}
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