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Simplifying 24a3 + 37a2 + -5a = 0 Reorder the terms: -5a + 37a2 + 24a3 = 0 Solving -5a + 37a2 + 24a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-5 + 37a + 24a2) = 0 Factor a trinomial. a((-5 + -3a)(1 + -8a)) = 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 '(-5 + -3a)' equal to zero and attempt to solve: Simplifying -5 + -3a = 0 Solving -5 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -3a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3a = 0 + 5 -3a = 0 + 5 Combine like terms: 0 + 5 = 5 -3a = 5 Divide each side by '-3'. a = -1.666666667 Simplifying a = -1.666666667Subproblem 3
Set the factor '(1 + -8a)' equal to zero and attempt to solve: Simplifying 1 + -8a = 0 Solving 1 + -8a = 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 + -8a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8a = 0 + -1 -8a = 0 + -1 Combine like terms: 0 + -1 = -1 -8a = -1 Divide each side by '-8'. a = 0.125 Simplifying a = 0.125Solution
a = {0, -1.666666667, 0.125}
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