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Simplifying (2a + 14)(3a + 12) = 0 Reorder the terms: (14 + 2a)(3a + 12) = 0 Reorder the terms: (14 + 2a)(12 + 3a) = 0 Multiply (14 + 2a) * (12 + 3a) (14(12 + 3a) + 2a * (12 + 3a)) = 0 ((12 * 14 + 3a * 14) + 2a * (12 + 3a)) = 0 ((168 + 42a) + 2a * (12 + 3a)) = 0 (168 + 42a + (12 * 2a + 3a * 2a)) = 0 (168 + 42a + (24a + 6a2)) = 0 Combine like terms: 42a + 24a = 66a (168 + 66a + 6a2) = 0 Solving 168 + 66a + 6a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '6'. 6(28 + 11a + a2) = 0 Factor a trinomial. 6((7 + a)(4 + a)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(7 + a)' equal to zero and attempt to solve: Simplifying 7 + a = 0 Solving 7 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + a = 0 + -7 a = 0 + -7 Combine like terms: 0 + -7 = -7 a = -7 Simplifying a = -7Subproblem 2
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 = -4Solution
a = {-7, -4}
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