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Simplifying (3a + 2)(2a + 5) = 0 Reorder the terms: (2 + 3a)(2a + 5) = 0 Reorder the terms: (2 + 3a)(5 + 2a) = 0 Multiply (2 + 3a) * (5 + 2a) (2(5 + 2a) + 3a * (5 + 2a)) = 0 ((5 * 2 + 2a * 2) + 3a * (5 + 2a)) = 0 ((10 + 4a) + 3a * (5 + 2a)) = 0 (10 + 4a + (5 * 3a + 2a * 3a)) = 0 (10 + 4a + (15a + 6a2)) = 0 Combine like terms: 4a + 15a = 19a (10 + 19a + 6a2) = 0 Solving 10 + 19a + 6a2 = 0 Solving for variable 'a'. Factor a trinomial. (5 + 2a)(2 + 3a) = 0Subproblem 1
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 = -2.5Subproblem 2
Set the factor '(2 + 3a)' equal to zero and attempt to solve: Simplifying 2 + 3a = 0 Solving 2 + 3a = 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 + 3a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3a = 0 + -2 3a = 0 + -2 Combine like terms: 0 + -2 = -2 3a = -2 Divide each side by '3'. a = -0.6666666667 Simplifying a = -0.6666666667Solution
a = {-2.5, -0.6666666667}
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