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Simplifying (a + 1)(a + 3) = 24 Reorder the terms: (1 + a)(a + 3) = 24 Reorder the terms: (1 + a)(3 + a) = 24 Multiply (1 + a) * (3 + a) (1(3 + a) + a(3 + a)) = 24 ((3 * 1 + a * 1) + a(3 + a)) = 24 ((3 + 1a) + a(3 + a)) = 24 (3 + 1a + (3 * a + a * a)) = 24 (3 + 1a + (3a + a2)) = 24 Combine like terms: 1a + 3a = 4a (3 + 4a + a2) = 24 Solving 3 + 4a + a2 = 24 Solving for variable 'a'. Reorder the terms: 3 + -24 + 4a + a2 = 24 + -24 Combine like terms: 3 + -24 = -21 -21 + 4a + a2 = 24 + -24 Combine like terms: 24 + -24 = 0 -21 + 4a + a2 = 0 Factor a trinomial. (-7 + -1a)(3 + -1a) = 0Subproblem 1
Set the factor '(-7 + -1a)' equal to zero and attempt to solve: Simplifying -7 + -1a = 0 Solving -7 + -1a = 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 + -1a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1a = 0 + 7 -1a = 0 + 7 Combine like terms: 0 + 7 = 7 -1a = 7 Divide each side by '-1'. a = -7 Simplifying a = -7Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve: Simplifying 3 + -1a = 0 Solving 3 + -1a = 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 + -1a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1a = 0 + -3 -1a = 0 + -3 Combine like terms: 0 + -3 = -3 -1a = -3 Divide each side by '-1'. a = 3 Simplifying a = 3Solution
a = {-7, 3}
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