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Simplifying 30a3 + -235a2 + 385a = 0 Reorder the terms: 385a + -235a2 + 30a3 = 0 Solving 385a + -235a2 + 30a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5a'. 5a(77 + -47a + 6a2) = 0 Factor a trinomial. 5a((7 + -3a)(11 + -2a)) = 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 '(7 + -3a)' equal to zero and attempt to solve: Simplifying 7 + -3a = 0 Solving 7 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3a = 0 + -7 -3a = 0 + -7 Combine like terms: 0 + -7 = -7 -3a = -7 Divide each side by '-3'. a = 2.333333333 Simplifying a = 2.333333333Subproblem 3
Set the factor '(11 + -2a)' equal to zero and attempt to solve: Simplifying 11 + -2a = 0 Solving 11 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -2a = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -2a = 0 + -11 -2a = 0 + -11 Combine like terms: 0 + -11 = -11 -2a = -11 Divide each side by '-2'. a = 5.5 Simplifying a = 5.5Solution
a = {0, 2.333333333, 5.5}
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