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Simplifying (7a + 7)(6a + 5) = 0 Reorder the terms: (7 + 7a)(6a + 5) = 0 Reorder the terms: (7 + 7a)(5 + 6a) = 0 Multiply (7 + 7a) * (5 + 6a) (7(5 + 6a) + 7a * (5 + 6a)) = 0 ((5 * 7 + 6a * 7) + 7a * (5 + 6a)) = 0 ((35 + 42a) + 7a * (5 + 6a)) = 0 (35 + 42a + (5 * 7a + 6a * 7a)) = 0 (35 + 42a + (35a + 42a2)) = 0 Combine like terms: 42a + 35a = 77a (35 + 77a + 42a2) = 0 Solving 35 + 77a + 42a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '7'. 7(5 + 11a + 6a2) = 0 Factor a trinomial. 7((1 + a)(5 + 6a)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(1 + a)' equal to zero and attempt to solve: Simplifying 1 + a = 0 Solving 1 + a = 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 + a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a = 0 + -1 a = 0 + -1 Combine like terms: 0 + -1 = -1 a = -1 Simplifying a = -1Subproblem 2
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 = {-1, -0.8333333333}
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