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Simplifying (2a + 3)(4a + 5) = 0 Reorder the terms: (3 + 2a)(4a + 5) = 0 Reorder the terms: (3 + 2a)(5 + 4a) = 0 Multiply (3 + 2a) * (5 + 4a) (3(5 + 4a) + 2a * (5 + 4a)) = 0 ((5 * 3 + 4a * 3) + 2a * (5 + 4a)) = 0 ((15 + 12a) + 2a * (5 + 4a)) = 0 (15 + 12a + (5 * 2a + 4a * 2a)) = 0 (15 + 12a + (10a + 8a2)) = 0 Combine like terms: 12a + 10a = 22a (15 + 22a + 8a2) = 0 Solving 15 + 22a + 8a2 = 0 Solving for variable 'a'. Factor a trinomial. (3 + 2a)(5 + 4a) = 0Subproblem 1
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 = -1.5Subproblem 2
Set the factor '(5 + 4a)' equal to zero and attempt to solve: Simplifying 5 + 4a = 0 Solving 5 + 4a = 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 + 4a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4a = 0 + -5 4a = 0 + -5 Combine like terms: 0 + -5 = -5 4a = -5 Divide each side by '4'. a = -1.25 Simplifying a = -1.25Solution
a = {-1.5, -1.25}
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