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Simplifying (2a + 1)(2a + 5) = 0 Reorder the terms: (1 + 2a)(2a + 5) = 0 Reorder the terms: (1 + 2a)(5 + 2a) = 0 Multiply (1 + 2a) * (5 + 2a) (1(5 + 2a) + 2a * (5 + 2a)) = 0 ((5 * 1 + 2a * 1) + 2a * (5 + 2a)) = 0 ((5 + 2a) + 2a * (5 + 2a)) = 0 (5 + 2a + (5 * 2a + 2a * 2a)) = 0 (5 + 2a + (10a + 4a2)) = 0 Combine like terms: 2a + 10a = 12a (5 + 12a + 4a2) = 0 Solving 5 + 12a + 4a2 = 0 Solving for variable 'a'. Factor a trinomial. (5 + 2a)(1 + 2a) = 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 '(1 + 2a)' equal to zero and attempt to solve: Simplifying 1 + 2a = 0 Solving 1 + 2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2a = 0 + -1 2a = 0 + -1 Combine like terms: 0 + -1 = -1 2a = -1 Divide each side by '2'. a = -0.5 Simplifying a = -0.5Solution
a = {-2.5, -0.5}
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