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Simplifying 6a3 + -18a2 + -1824a = 0 Reorder the terms: -1824a + -18a2 + 6a3 = 0 Solving -1824a + -18a2 + 6a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '6a'. 6a(-304 + -3a + a2) = 0 Factor a trinomial. 6a((-16 + -1a)(19 + -1a)) = 0 Ignore the factor 6.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 '(-16 + -1a)' equal to zero and attempt to solve: Simplifying -16 + -1a = 0 Solving -16 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -1a = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1a = 0 + 16 -1a = 0 + 16 Combine like terms: 0 + 16 = 16 -1a = 16 Divide each side by '-1'. a = -16 Simplifying a = -16Subproblem 3
Set the factor '(19 + -1a)' equal to zero and attempt to solve: Simplifying 19 + -1a = 0 Solving 19 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -1a = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -1a = 0 + -19 -1a = 0 + -19 Combine like terms: 0 + -19 = -19 -1a = -19 Divide each side by '-1'. a = 19 Simplifying a = 19Solution
a = {0, -16, 19}
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