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Simplifying a(a + 11)(6a + 5) = 0 Reorder the terms: a(11 + a)(6a + 5) = 0 Reorder the terms: a(11 + a)(5 + 6a) = 0 Multiply (11 + a) * (5 + 6a) a(11(5 + 6a) + a(5 + 6a)) = 0 a((5 * 11 + 6a * 11) + a(5 + 6a)) = 0 a((55 + 66a) + a(5 + 6a)) = 0 a(55 + 66a + (5 * a + 6a * a)) = 0 a(55 + 66a + (5a + 6a2)) = 0 Combine like terms: 66a + 5a = 71a a(55 + 71a + 6a2) = 0 (55 * a + 71a * a + 6a2 * a) = 0 (55a + 71a2 + 6a3) = 0 Solving 55a + 71a2 + 6a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(55 + 71a + 6a2) = 0 Factor a trinomial. a((11 + a)(5 + 6a)) = 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 '(11 + a)' equal to zero and attempt to solve: Simplifying 11 + a = 0 Solving 11 + a = 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 + a = 0 + -11 Combine like terms: 11 + -11 = 0 0 + a = 0 + -11 a = 0 + -11 Combine like terms: 0 + -11 = -11 a = -11 Simplifying a = -11Subproblem 3
Set the factor '(5 + 6a)' equal to zero and attempt to solve: Simplifying 5 + 6a = 0 Solving 5 + 6a = 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 + 6a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6a = 0 + -5 6a = 0 + -5 Combine like terms: 0 + -5 = -5 6a = -5 Divide each side by '6'. a = -0.8333333333 Simplifying a = -0.8333333333Solution
a = {0, -11, -0.8333333333}
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