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Simplifying 5a(16a2 + 24a + 9) = 0 Reorder the terms: 5a(9 + 24a + 16a2) = 0 (9 * 5a + 24a * 5a + 16a2 * 5a) = 0 (45a + 120a2 + 80a3) = 0 Solving 45a + 120a2 + 80a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5a'. 5a(9 + 24a + 16a2) = 0 Factor a trinomial. 5a((3 + 4a)(3 + 4a)) = 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 '(3 + 4a)' equal to zero and attempt to solve: Simplifying 3 + 4a = 0 Solving 3 + 4a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4a = 0 + -3 4a = 0 + -3 Combine like terms: 0 + -3 = -3 4a = -3 Divide each side by '4'. a = -0.75 Simplifying a = -0.75Subproblem 3
Set the factor '(3 + 4a)' equal to zero and attempt to solve: Simplifying 3 + 4a = 0 Solving 3 + 4a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4a = 0 + -3 4a = 0 + -3 Combine like terms: 0 + -3 = -3 4a = -3 Divide each side by '4'. a = -0.75 Simplifying a = -0.75Solution
a = {0, -0.75, -0.75}
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