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Simplifying (2a + 6)(a + 7) = 0 Reorder the terms: (6 + 2a)(a + 7) = 0 Reorder the terms: (6 + 2a)(7 + a) = 0 Multiply (6 + 2a) * (7 + a) (6(7 + a) + 2a * (7 + a)) = 0 ((7 * 6 + a * 6) + 2a * (7 + a)) = 0 ((42 + 6a) + 2a * (7 + a)) = 0 (42 + 6a + (7 * 2a + a * 2a)) = 0 (42 + 6a + (14a + 2a2)) = 0 Combine like terms: 6a + 14a = 20a (42 + 20a + 2a2) = 0 Solving 42 + 20a + 2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 10a + a2) = 0 Factor a trinomial. 2((7 + a)(3 + a)) = 0 Ignore the factor 2.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 '(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 = -3Solution
a = {-7, -3}
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