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Simplifying 3a3 + -9a2 + -54a = 0 Reorder the terms: -54a + -9a2 + 3a3 = 0 Solving -54a + -9a2 + 3a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a'. 3a(-18 + -3a + a2) = 0 Factor a trinomial. 3a((-3 + -1a)(6 + -1a)) = 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 '(-3 + -1a)' equal to zero and attempt to solve: Simplifying -3 + -1a = 0 Solving -3 + -1a = 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 + -1a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1a = 0 + 3 -1a = 0 + 3 Combine like terms: 0 + 3 = 3 -1a = 3 Divide each side by '-1'. a = -3 Simplifying a = -3Subproblem 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, -3, 6}
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