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Simplifying (3a + 7)(a + 6) = 0 Reorder the terms: (7 + 3a)(a + 6) = 0 Reorder the terms: (7 + 3a)(6 + a) = 0 Multiply (7 + 3a) * (6 + a) (7(6 + a) + 3a * (6 + a)) = 0 ((6 * 7 + a * 7) + 3a * (6 + a)) = 0 ((42 + 7a) + 3a * (6 + a)) = 0 (42 + 7a + (6 * 3a + a * 3a)) = 0 (42 + 7a + (18a + 3a2)) = 0 Combine like terms: 7a + 18a = 25a (42 + 25a + 3a2) = 0 Solving 42 + 25a + 3a2 = 0 Solving for variable 'a'. Factor a trinomial. (6 + a)(7 + 3a) = 0Subproblem 1
Set the factor '(6 + a)' equal to zero and attempt to solve: Simplifying 6 + a = 0 Solving 6 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = 0 + -6 Combine like terms: 6 + -6 = 0 0 + a = 0 + -6 a = 0 + -6 Combine like terms: 0 + -6 = -6 a = -6 Simplifying a = -6Subproblem 2
Set the factor '(7 + 3a)' equal to zero and attempt to solve: Simplifying 7 + 3a = 0 Solving 7 + 3a = 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 + 3a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3a = 0 + -7 3a = 0 + -7 Combine like terms: 0 + -7 = -7 3a = -7 Divide each side by '3'. a = -2.333333333 Simplifying a = -2.333333333Solution
a = {-6, -2.333333333}
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