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Simplifying 16a3 + 32a2 + 12a = 0 Reorder the terms: 12a + 32a2 + 16a3 = 0 Solving 12a + 32a2 + 16a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4a'. 4a(3 + 8a + 4a2) = 0 Factor a trinomial. 4a((3 + 2a)(1 + 2a)) = 0 Ignore the factor 4.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 + 2a)' equal to zero and attempt to solve: Simplifying 3 + 2a = 0 Solving 3 + 2a = 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 + 2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2a = 0 + -3 2a = 0 + -3 Combine like terms: 0 + -3 = -3 2a = -3 Divide each side by '2'. a = -1.5 Simplifying a = -1.5Subproblem 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, -1.5, -0.5}
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