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Simplifying (a + 3)(a + 6) = -2 Reorder the terms: (3 + a)(a + 6) = -2 Reorder the terms: (3 + a)(6 + a) = -2 Multiply (3 + a) * (6 + a) (3(6 + a) + a(6 + a)) = -2 ((6 * 3 + a * 3) + a(6 + a)) = -2 ((18 + 3a) + a(6 + a)) = -2 (18 + 3a + (6 * a + a * a)) = -2 (18 + 3a + (6a + a2)) = -2 Combine like terms: 3a + 6a = 9a (18 + 9a + a2) = -2 Solving 18 + 9a + a2 = -2 Solving for variable 'a'. Reorder the terms: 18 + 2 + 9a + a2 = -2 + 2 Combine like terms: 18 + 2 = 20 20 + 9a + a2 = -2 + 2 Combine like terms: -2 + 2 = 0 20 + 9a + a2 = 0 Factor a trinomial. (5 + a)(4 + a) = 0Subproblem 1
Set the factor '(5 + a)' equal to zero and attempt to solve: Simplifying 5 + a = 0 Solving 5 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + a = 0 + -5 a = 0 + -5 Combine like terms: 0 + -5 = -5 a = -5 Simplifying a = -5Subproblem 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 = {-5, -4}
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