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Simplifying 54a3 + 63a2 + -216a = 0 Reorder the terms: -216a + 63a2 + 54a3 = 0 Solving -216a + 63a2 + 54a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '9a'. 9a(-24 + 7a + 6a2) = 0 Factor a trinomial. 9a((-8 + -3a)(3 + -2a)) = 0 Ignore the factor 9.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 '(-8 + -3a)' equal to zero and attempt to solve: Simplifying -8 + -3a = 0 Solving -8 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3a = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3a = 0 + 8 -3a = 0 + 8 Combine like terms: 0 + 8 = 8 -3a = 8 Divide each side by '-3'. a = -2.666666667 Simplifying a = -2.666666667Subproblem 3
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 = 1.5Solution
a = {0, -2.666666667, 1.5}
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