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Simplifying 3a3 = 14a2 + 24a Reorder the terms: 3a3 = 24a + 14a2 Solving 3a3 = 24a + 14a2 Solving for variable 'a'. Reorder the terms: -24a + -14a2 + 3a3 = 24a + 14a2 + -24a + -14a2 Reorder the terms: -24a + -14a2 + 3a3 = 24a + -24a + 14a2 + -14a2 Combine like terms: 24a + -24a = 0 -24a + -14a2 + 3a3 = 0 + 14a2 + -14a2 -24a + -14a2 + 3a3 = 14a2 + -14a2 Combine like terms: 14a2 + -14a2 = 0 -24a + -14a2 + 3a3 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(-24 + -14a + 3a2) = 0 Factor a trinomial. a((-4 + -3a)(6 + -1a)) = 0Subproblem 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 '(6 + -1a)' equal to zero and attempt to solve: Simplifying 6 + -1a = 0 Solving 6 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1a = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1a = 0 + -6 -1a = 0 + -6 Combine like terms: 0 + -6 = -6 -1a = -6 Divide each side by '-1'. a = 6 Simplifying a = 6Solution
a = {0, -1.333333333, 6}
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