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Simplifying (a + 5)(a + 6) = 0 Reorder the terms: (5 + a)(a + 6) = 0 Reorder the terms: (5 + a)(6 + a) = 0 Multiply (5 + a) * (6 + a) (5(6 + a) + a(6 + a)) = 0 ((6 * 5 + a * 5) + a(6 + a)) = 0 ((30 + 5a) + a(6 + a)) = 0 (30 + 5a + (6 * a + a * a)) = 0 (30 + 5a + (6a + a2)) = 0 Combine like terms: 5a + 6a = 11a (30 + 11a + a2) = 0 Solving 30 + 11a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (6 + a)(5 + a) = 0Subproblem 1
Set the factor '(6 + a)' equal to zero and attempt to solve: Simplifying 6 + a = 0 Solving 6 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = 0 + -6 Combine like terms: 6 + -6 = 0 0 + a = 0 + -6 a = 0 + -6 Combine like terms: 0 + -6 = -6 a = -6 Simplifying a = -6Subproblem 2
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 = -5Solution
a = {-6, -5}
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