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Simplifying -6a3 + 18a + -9a2 = 3a3 + 9a2 + -9a Reorder the terms: 18a + -9a2 + -6a3 = 3a3 + 9a2 + -9a Reorder the terms: 18a + -9a2 + -6a3 = -9a + 9a2 + 3a3 Solving 18a + -9a2 + -6a3 = -9a + 9a2 + 3a3 Solving for variable 'a'. Reorder the terms: 18a + 9a + -9a2 + -9a2 + -6a3 + -3a3 = -9a + 9a2 + 3a3 + 9a + -9a2 + -3a3 Combine like terms: 18a + 9a = 27a 27a + -9a2 + -9a2 + -6a3 + -3a3 = -9a + 9a2 + 3a3 + 9a + -9a2 + -3a3 Combine like terms: -9a2 + -9a2 = -18a2 27a + -18a2 + -6a3 + -3a3 = -9a + 9a2 + 3a3 + 9a + -9a2 + -3a3 Combine like terms: -6a3 + -3a3 = -9a3 27a + -18a2 + -9a3 = -9a + 9a2 + 3a3 + 9a + -9a2 + -3a3 Reorder the terms: 27a + -18a2 + -9a3 = -9a + 9a + 9a2 + -9a2 + 3a3 + -3a3 Combine like terms: -9a + 9a = 0 27a + -18a2 + -9a3 = 0 + 9a2 + -9a2 + 3a3 + -3a3 27a + -18a2 + -9a3 = 9a2 + -9a2 + 3a3 + -3a3 Combine like terms: 9a2 + -9a2 = 0 27a + -18a2 + -9a3 = 0 + 3a3 + -3a3 27a + -18a2 + -9a3 = 3a3 + -3a3 Combine like terms: 3a3 + -3a3 = 0 27a + -18a2 + -9a3 = 0 Factor out the Greatest Common Factor (GCF), '9a'. 9a(3 + -2a + -1a2) = 0 Factor a trinomial. 9a((1 + -1a)(3 + a)) = 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 '(1 + -1a)' equal to zero and attempt to solve: Simplifying 1 + -1a = 0 Solving 1 + -1a = 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 + -1a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a = 0 + -1 -1a = 0 + -1 Combine like terms: 0 + -1 = -1 -1a = -1 Divide each side by '-1'. a = 1 Simplifying a = 1Subproblem 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, -3}
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