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Simplifying (2a + 5)(a + 4) = 0 Reorder the terms: (5 + 2a)(a + 4) = 0 Reorder the terms: (5 + 2a)(4 + a) = 0 Multiply (5 + 2a) * (4 + a) (5(4 + a) + 2a * (4 + a)) = 0 ((4 * 5 + a * 5) + 2a * (4 + a)) = 0 ((20 + 5a) + 2a * (4 + a)) = 0 (20 + 5a + (4 * 2a + a * 2a)) = 0 (20 + 5a + (8a + 2a2)) = 0 Combine like terms: 5a + 8a = 13a (20 + 13a + 2a2) = 0 Solving 20 + 13a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (4 + a)(5 + 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 '(5 + 2a)' equal to zero and attempt to solve: Simplifying 5 + 2a = 0 Solving 5 + 2a = 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 + 2a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2a = 0 + -5 2a = 0 + -5 Combine like terms: 0 + -5 = -5 2a = -5 Divide each side by '2'. a = -2.5 Simplifying a = -2.5Solution
a = {-4, -2.5}
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