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Simplifying (a + 6)(a + 4) = 3 Reorder the terms: (6 + a)(a + 4) = 3 Reorder the terms: (6 + a)(4 + a) = 3 Multiply (6 + a) * (4 + a) (6(4 + a) + a(4 + a)) = 3 ((4 * 6 + a * 6) + a(4 + a)) = 3 ((24 + 6a) + a(4 + a)) = 3 (24 + 6a + (4 * a + a * a)) = 3 (24 + 6a + (4a + a2)) = 3 Combine like terms: 6a + 4a = 10a (24 + 10a + a2) = 3 Solving 24 + 10a + a2 = 3 Solving for variable 'a'. Reorder the terms: 24 + -3 + 10a + a2 = 3 + -3 Combine like terms: 24 + -3 = 21 21 + 10a + a2 = 3 + -3 Combine like terms: 3 + -3 = 0 21 + 10a + a2 = 0 Factor a trinomial. (7 + a)(3 + a) = 0Subproblem 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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