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Simplifying 5a3 + 20a2 + -60a = 0 Reorder the terms: -60a + 20a2 + 5a3 = 0 Solving -60a + 20a2 + 5a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5a'. 5a(-12 + 4a + a2) = 0 Factor a trinomial. 5a((-6 + -1a)(2 + -1a)) = 0 Ignore the factor 5.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 '(-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 = -6Subproblem 3
Set the factor '(2 + -1a)' equal to zero and attempt to solve: Simplifying 2 + -1a = 0 Solving 2 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a = 0 + -2 -1a = 0 + -2 Combine like terms: 0 + -2 = -2 -1a = -2 Divide each side by '-1'. a = 2 Simplifying a = 2Solution
a = {0, -6, 2}
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