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Simplifying 5a(5a + 4)(2a + 1) = 0 Reorder the terms: 5a(4 + 5a)(2a + 1) = 0 Reorder the terms: 5a(4 + 5a)(1 + 2a) = 0 Multiply (4 + 5a) * (1 + 2a) 5a(4(1 + 2a) + 5a * (1 + 2a)) = 0 5a((1 * 4 + 2a * 4) + 5a * (1 + 2a)) = 0 5a((4 + 8a) + 5a * (1 + 2a)) = 0 5a(4 + 8a + (1 * 5a + 2a * 5a)) = 0 5a(4 + 8a + (5a + 10a2)) = 0 Combine like terms: 8a + 5a = 13a 5a(4 + 13a + 10a2) = 0 (4 * 5a + 13a * 5a + 10a2 * 5a) = 0 (20a + 65a2 + 50a3) = 0 Solving 20a + 65a2 + 50a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5a'. 5a(4 + 13a + 10a2) = 0 Factor a trinomial. 5a((4 + 5a)(1 + 2a)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 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 = -0.8Subproblem 3
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 = {0, -0.8, -0.5}
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