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Simplifying (6a + 7)(6a + 5) = 0 Reorder the terms: (7 + 6a)(6a + 5) = 0 Reorder the terms: (7 + 6a)(5 + 6a) = 0 Multiply (7 + 6a) * (5 + 6a) (7(5 + 6a) + 6a * (5 + 6a)) = 0 ((5 * 7 + 6a * 7) + 6a * (5 + 6a)) = 0 ((35 + 42a) + 6a * (5 + 6a)) = 0 (35 + 42a + (5 * 6a + 6a * 6a)) = 0 (35 + 42a + (30a + 36a2)) = 0 Combine like terms: 42a + 30a = 72a (35 + 72a + 36a2) = 0 Solving 35 + 72a + 36a2 = 0 Solving for variable 'a'. Factor a trinomial. (7 + 6a)(5 + 6a) = 0Subproblem 1
Set the factor '(7 + 6a)' equal to zero and attempt to solve: Simplifying 7 + 6a = 0 Solving 7 + 6a = 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 + 6a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6a = 0 + -7 6a = 0 + -7 Combine like terms: 0 + -7 = -7 6a = -7 Divide each side by '6'. a = -1.166666667 Simplifying a = -1.166666667Subproblem 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 = {-1.166666667, -0.8333333333}
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