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Simplifying 0 = 6a3 + 10a2 + -24a Reorder the terms: 0 = -24a + 10a2 + 6a3 Solving 0 = -24a + 10a2 + 6a3 Solving for variable 'a'. Remove the zero: 24a + -10a2 + -6a3 = -24a + 10a2 + 6a3 + 24a + -10a2 + -6a3 Reorder the terms: 24a + -10a2 + -6a3 = -24a + 24a + 10a2 + -10a2 + 6a3 + -6a3 Combine like terms: -24a + 24a = 0 24a + -10a2 + -6a3 = 0 + 10a2 + -10a2 + 6a3 + -6a3 24a + -10a2 + -6a3 = 10a2 + -10a2 + 6a3 + -6a3 Combine like terms: 10a2 + -10a2 = 0 24a + -10a2 + -6a3 = 0 + 6a3 + -6a3 24a + -10a2 + -6a3 = 6a3 + -6a3 Combine like terms: 6a3 + -6a3 = 0 24a + -10a2 + -6a3 = 0 Factor out the Greatest Common Factor (GCF), '2a'. 2a(12 + -5a + -3a2) = 0 Factor a trinomial. 2a((4 + -3a)(3 + a)) = 0 Ignore the factor 2.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 '(4 + -3a)' equal to zero and attempt to solve: Simplifying 4 + -3a = 0 Solving 4 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3a = 0 + -4 -3a = 0 + -4 Combine like terms: 0 + -4 = -4 -3a = -4 Divide each side by '-3'. a = 1.333333333 Simplifying a = 1.333333333Subproblem 3
Set the factor '(3 + a)' equal to zero and attempt to solve: Simplifying 3 + a = 0 Solving 3 + a = 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 + a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + a = 0 + -3 a = 0 + -3 Combine like terms: 0 + -3 = -3 a = -3 Simplifying a = -3Solution
a = {0, 1.333333333, -3}
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