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Simplifying (6a + 13)(a + 12) = 0 Reorder the terms: (13 + 6a)(a + 12) = 0 Reorder the terms: (13 + 6a)(12 + a) = 0 Multiply (13 + 6a) * (12 + a) (13(12 + a) + 6a * (12 + a)) = 0 ((12 * 13 + a * 13) + 6a * (12 + a)) = 0 ((156 + 13a) + 6a * (12 + a)) = 0 (156 + 13a + (12 * 6a + a * 6a)) = 0 (156 + 13a + (72a + 6a2)) = 0 Combine like terms: 13a + 72a = 85a (156 + 85a + 6a2) = 0 Solving 156 + 85a + 6a2 = 0 Solving for variable 'a'. Factor a trinomial. (12 + a)(13 + 6a) = 0Subproblem 1
Set the factor '(12 + a)' equal to zero and attempt to solve: Simplifying 12 + a = 0 Solving 12 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + a = 0 + -12 Combine like terms: 12 + -12 = 0 0 + a = 0 + -12 a = 0 + -12 Combine like terms: 0 + -12 = -12 a = -12 Simplifying a = -12Subproblem 2
Set the factor '(13 + 6a)' equal to zero and attempt to solve: Simplifying 13 + 6a = 0 Solving 13 + 6a = 0 Move all terms containing a to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 6a = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 6a = 0 + -13 6a = 0 + -13 Combine like terms: 0 + -13 = -13 6a = -13 Divide each side by '6'. a = -2.166666667 Simplifying a = -2.166666667Solution
a = {-12, -2.166666667}
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