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Simplifying (a + 1)(a + 7) = 0 Reorder the terms: (1 + a)(a + 7) = 0 Reorder the terms: (1 + a)(7 + a) = 0 Multiply (1 + a) * (7 + a) (1(7 + a) + a(7 + a)) = 0 ((7 * 1 + a * 1) + a(7 + a)) = 0 ((7 + 1a) + a(7 + a)) = 0 (7 + 1a + (7 * a + a * a)) = 0 (7 + 1a + (7a + a2)) = 0 Combine like terms: 1a + 7a = 8a (7 + 8a + a2) = 0 Solving 7 + 8a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (7 + a)(1 + 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 '(1 + a)' equal to zero and attempt to solve: Simplifying 1 + a = 0 Solving 1 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a = 0 + -1 a = 0 + -1 Combine like terms: 0 + -1 = -1 a = -1 Simplifying a = -1Solution
a = {-7, -1}
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