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Simplifying 36a3 + 19a2 + -6a = 0 Reorder the terms: -6a + 19a2 + 36a3 = 0 Solving -6a + 19a2 + 36a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-6 + 19a + 36a2) = 0 Factor a trinomial. a((-3 + -4a)(2 + -9a)) = 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 '(-3 + -4a)' equal to zero and attempt to solve: Simplifying -3 + -4a = 0 Solving -3 + -4a = 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 + -4a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4a = 0 + 3 -4a = 0 + 3 Combine like terms: 0 + 3 = 3 -4a = 3 Divide each side by '-4'. a = -0.75 Simplifying a = -0.75Subproblem 3
Set the factor '(2 + -9a)' equal to zero and attempt to solve: Simplifying 2 + -9a = 0 Solving 2 + -9a = 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 + -9a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9a = 0 + -2 -9a = 0 + -2 Combine like terms: 0 + -2 = -2 -9a = -2 Divide each side by '-9'. a = 0.2222222222 Simplifying a = 0.2222222222Solution
a = {0, -0.75, 0.2222222222}
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