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Simplifying 24a3 + -66a2 + 15a = 0 Reorder the terms: 15a + -66a2 + 24a3 = 0 Solving 15a + -66a2 + 24a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a'. 3a(5 + -22a + 8a2) = 0 Factor a trinomial. 3a((1 + -4a)(5 + -2a)) = 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 '(1 + -4a)' equal to zero and attempt to solve: Simplifying 1 + -4a = 0 Solving 1 + -4a = 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 + -4a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4a = 0 + -1 -4a = 0 + -1 Combine like terms: 0 + -1 = -1 -4a = -1 Divide each side by '-4'. a = 0.25 Simplifying a = 0.25Subproblem 3
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 = 2.5Solution
a = {0, 0.25, 2.5}
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