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Simplifying 2(3a2 + 13a + 12) = 0 Reorder the terms: 2(12 + 13a + 3a2) = 0 (12 * 2 + 13a * 2 + 3a2 * 2) = 0 (24 + 26a + 6a2) = 0 Solving 24 + 26a + 6a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 13a + 3a2) = 0 Factor a trinomial. 2((3 + a)(4 + 3a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + a)' equal to zero and attempt to solve: Simplifying 3 + a = 0 Solving 3 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + a = 0 + -3 a = 0 + -3 Combine like terms: 0 + -3 = -3 a = -3 Simplifying a = -3Subproblem 2
Set the factor '(4 + 3a)' equal to zero and attempt to solve: Simplifying 4 + 3a = 0 Solving 4 + 3a = 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 + 3a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3a = 0 + -4 3a = 0 + -4 Combine like terms: 0 + -4 = -4 3a = -4 Divide each side by '3'. a = -1.333333333 Simplifying a = -1.333333333Solution
a = {-3, -1.333333333}
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