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Simplifying 9a3 + 91a2 + 90a = 0 Reorder the terms: 90a + 91a2 + 9a3 = 0 Solving 90a + 91a2 + 9a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(90 + 91a + 9a2) = 0 Factor a trinomial. a((9 + a)(10 + 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 '(9 + a)' equal to zero and attempt to solve: Simplifying 9 + a = 0 Solving 9 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + a = 0 + -9 Combine like terms: 9 + -9 = 0 0 + a = 0 + -9 a = 0 + -9 Combine like terms: 0 + -9 = -9 a = -9 Simplifying a = -9Subproblem 3
Set the factor '(10 + 9a)' equal to zero and attempt to solve: Simplifying 10 + 9a = 0 Solving 10 + 9a = 0 Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 9a = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 9a = 0 + -10 9a = 0 + -10 Combine like terms: 0 + -10 = -10 9a = -10 Divide each side by '9'. a = -1.111111111 Simplifying a = -1.111111111Solution
a = {0, -9, -1.111111111}
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