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Simplifying (a + 5)(a + 3) = 0 Reorder the terms: (5 + a)(a + 3) = 0 Reorder the terms: (5 + a)(3 + a) = 0 Multiply (5 + a) * (3 + a) (5(3 + a) + a(3 + a)) = 0 ((3 * 5 + a * 5) + a(3 + a)) = 0 ((15 + 5a) + a(3 + a)) = 0 (15 + 5a + (3 * a + a * a)) = 0 (15 + 5a + (3a + a2)) = 0 Combine like terms: 5a + 3a = 8a (15 + 8a + a2) = 0 Solving 15 + 8a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (5 + a)(3 + 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 '(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 = {-5, -3}
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