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Simplifying (2a + 1)(3a + 12) = 0 Reorder the terms: (1 + 2a)(3a + 12) = 0 Reorder the terms: (1 + 2a)(12 + 3a) = 0 Multiply (1 + 2a) * (12 + 3a) (1(12 + 3a) + 2a * (12 + 3a)) = 0 ((12 * 1 + 3a * 1) + 2a * (12 + 3a)) = 0 ((12 + 3a) + 2a * (12 + 3a)) = 0 (12 + 3a + (12 * 2a + 3a * 2a)) = 0 (12 + 3a + (24a + 6a2)) = 0 Combine like terms: 3a + 24a = 27a (12 + 27a + 6a2) = 0 Solving 12 + 27a + 6a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 9a + 2a2) = 0 Factor a trinomial. 3((4 + a)(1 + 2a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + a)' equal to zero and attempt to solve: Simplifying 4 + a = 0 Solving 4 + a = 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 + a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + a = 0 + -4 a = 0 + -4 Combine like terms: 0 + -4 = -4 a = -4 Simplifying a = -4Subproblem 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 = {-4, -0.5}
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