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Simplifying (3a + 6)(5a + 10) = 0 Reorder the terms: (6 + 3a)(5a + 10) = 0 Reorder the terms: (6 + 3a)(10 + 5a) = 0 Multiply (6 + 3a) * (10 + 5a) (6(10 + 5a) + 3a * (10 + 5a)) = 0 ((10 * 6 + 5a * 6) + 3a * (10 + 5a)) = 0 ((60 + 30a) + 3a * (10 + 5a)) = 0 (60 + 30a + (10 * 3a + 5a * 3a)) = 0 (60 + 30a + (30a + 15a2)) = 0 Combine like terms: 30a + 30a = 60a (60 + 60a + 15a2) = 0 Solving 60 + 60a + 15a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '15'. 15(4 + 4a + a2) = 0 Factor a trinomial. 15((2 + a)(2 + a)) = 0 Ignore the factor 15.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 '(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 = -2Solution
a = {-2, -2}
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