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Simplifying (3a + 6)(5a + 4) = 0 Reorder the terms: (6 + 3a)(5a + 4) = 0 Reorder the terms: (6 + 3a)(4 + 5a) = 0 Multiply (6 + 3a) * (4 + 5a) (6(4 + 5a) + 3a * (4 + 5a)) = 0 ((4 * 6 + 5a * 6) + 3a * (4 + 5a)) = 0 ((24 + 30a) + 3a * (4 + 5a)) = 0 (24 + 30a + (4 * 3a + 5a * 3a)) = 0 (24 + 30a + (12a + 15a2)) = 0 Combine like terms: 30a + 12a = 42a (24 + 42a + 15a2) = 0 Solving 24 + 42a + 15a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(8 + 14a + 5a2) = 0 Factor a trinomial. 3((2 + a)(4 + 5a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + a)' equal to zero and attempt to solve: Simplifying 2 + a = 0 Solving 2 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + a = 0 + -2 a = 0 + -2 Combine like terms: 0 + -2 = -2 a = -2 Simplifying a = -2Subproblem 2
Set the factor '(4 + 5a)' equal to zero and attempt to solve: Simplifying 4 + 5a = 0 Solving 4 + 5a = 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 + 5a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5a = 0 + -4 5a = 0 + -4 Combine like terms: 0 + -4 = -4 5a = -4 Divide each side by '5'. a = -0.8 Simplifying a = -0.8Solution
a = {-2, -0.8}
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