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Simplifying -48a3 + -24a2 + 45a = 0 Reorder the terms: 45a + -24a2 + -48a3 = 0 Solving 45a + -24a2 + -48a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a'. 3a(15 + -8a + -16a2) = 0 Factor a trinomial. 3a((3 + -4a)(5 + 4a)) = 0 Ignore the factor 3.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 '(5 + 4a)' equal to zero and attempt to solve: Simplifying 5 + 4a = 0 Solving 5 + 4a = 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 + 4a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4a = 0 + -5 4a = 0 + -5 Combine like terms: 0 + -5 = -5 4a = -5 Divide each side by '4'. a = -1.25 Simplifying a = -1.25Solution
a = {0, 0.75, -1.25}
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