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Simplifying 20a3 + -41a2 + 20a = 0 Reorder the terms: 20a + -41a2 + 20a3 = 0 Solving 20a + -41a2 + 20a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(20 + -41a + 20a2) = 0 Factor a trinomial. a((4 + -5a)(5 + -4a)) = 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 '(4 + -5a)' equal to zero and attempt to solve: Simplifying 4 + -5a = 0 Solving 4 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5a = 0 + -4 -5a = 0 + -4 Combine like terms: 0 + -4 = -4 -5a = -4 Divide each side by '-5'. a = 0.8 Simplifying a = 0.8Subproblem 3
Set the factor '(5 + -4a)' equal to zero and attempt to solve: Simplifying 5 + -4a = 0 Solving 5 + -4a = 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 + -4a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4a = 0 + -5 -4a = 0 + -5 Combine like terms: 0 + -5 = -5 -4a = -5 Divide each side by '-4'. a = 1.25 Simplifying a = 1.25Solution
a = {0, 0.8, 1.25}
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