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Simplifying -8a2 + -1(a + -1(20a2 + 8a)) + -1(5 + (6a + -5)) = 0 Reorder the terms: -8a2 + -1(a + -1(8a + 20a2)) + -1(5 + (6a + -5)) = 0 -8a2 + -1(a + (8a * -1 + 20a2 * -1)) + -1(5 + (6a + -5)) = 0 -8a2 + -1(a + (-8a + -20a2)) + -1(5 + (6a + -5)) = 0 Combine like terms: a + -8a = -7a -8a2 + -1(-7a + -20a2) + -1(5 + (6a + -5)) = 0 -8a2 + (-7a * -1 + -20a2 * -1) + -1(5 + (6a + -5)) = 0 -8a2 + (7a + 20a2) + -1(5 + (6a + -5)) = 0 Reorder the terms: -8a2 + 7a + 20a2 + -1(5 + (-5 + 6a)) = 0 Remove parenthesis around (-5 + 6a) -8a2 + 7a + 20a2 + -1(5 + -5 + 6a) = 0 Combine like terms: 5 + -5 = 0 -8a2 + 7a + 20a2 + -1(0 + 6a) = 0 -8a2 + 7a + 20a2 + -1(6a) = 0 Remove parenthesis around (6a) -8a2 + 7a + 20a2 + -1 * 6a = 0 Multiply -1 * 6 -8a2 + 7a + 20a2 + -6a = 0 Reorder the terms: 7a + -6a + -8a2 + 20a2 = 0 Combine like terms: 7a + -6a = 1a 1a + -8a2 + 20a2 = 0 Combine like terms: -8a2 + 20a2 = 12a2 1a + 12a2 = 0 Solving 1a + 12a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(1 + 12a) = 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 '(1 + 12a)' equal to zero and attempt to solve: Simplifying 1 + 12a = 0 Solving 1 + 12a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 12a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 12a = 0 + -1 12a = 0 + -1 Combine like terms: 0 + -1 = -1 12a = -1 Divide each side by '12'. a = -0.08333333333 Simplifying a = -0.08333333333Solution
a = {0, -0.08333333333}
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