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Simplifying (4a + 9)(a + 4) = 0 Reorder the terms: (9 + 4a)(a + 4) = 0 Reorder the terms: (9 + 4a)(4 + a) = 0 Multiply (9 + 4a) * (4 + a) (9(4 + a) + 4a * (4 + a)) = 0 ((4 * 9 + a * 9) + 4a * (4 + a)) = 0 ((36 + 9a) + 4a * (4 + a)) = 0 (36 + 9a + (4 * 4a + a * 4a)) = 0 (36 + 9a + (16a + 4a2)) = 0 Combine like terms: 9a + 16a = 25a (36 + 25a + 4a2) = 0 Solving 36 + 25a + 4a2 = 0 Solving for variable 'a'. Factor a trinomial. (4 + a)(9 + 4a) = 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 '(9 + 4a)' equal to zero and attempt to solve: Simplifying 9 + 4a = 0 Solving 9 + 4a = 0 Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4a = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4a = 0 + -9 4a = 0 + -9 Combine like terms: 0 + -9 = -9 4a = -9 Divide each side by '4'. a = -2.25 Simplifying a = -2.25Solution
a = {-4, -2.25}
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