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Simplifying (2a + 3)(a + 4) = 0 Reorder the terms: (3 + 2a)(a + 4) = 0 Reorder the terms: (3 + 2a)(4 + a) = 0 Multiply (3 + 2a) * (4 + a) (3(4 + a) + 2a * (4 + a)) = 0 ((4 * 3 + a * 3) + 2a * (4 + a)) = 0 ((12 + 3a) + 2a * (4 + a)) = 0 (12 + 3a + (4 * 2a + a * 2a)) = 0 (12 + 3a + (8a + 2a2)) = 0 Combine like terms: 3a + 8a = 11a (12 + 11a + 2a2) = 0 Solving 12 + 11a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (4 + a)(3 + 2a) = 0Subproblem 1
Set the factor '(4 + a)' equal to zero and attempt to solve: Simplifying 4 + a = 0 Solving 4 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + a = 0 + -4 a = 0 + -4 Combine like terms: 0 + -4 = -4 a = -4 Simplifying a = -4Subproblem 2
Set the factor '(3 + 2a)' equal to zero and attempt to solve: Simplifying 3 + 2a = 0 Solving 3 + 2a = 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 + 2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2a = 0 + -3 2a = 0 + -3 Combine like terms: 0 + -3 = -3 2a = -3 Divide each side by '2'. a = -1.5 Simplifying a = -1.5Solution
a = {-4, -1.5}
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