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Simplifying (2a + 3)(6a + 7) = 0 Reorder the terms: (3 + 2a)(6a + 7) = 0 Reorder the terms: (3 + 2a)(7 + 6a) = 0 Multiply (3 + 2a) * (7 + 6a) (3(7 + 6a) + 2a * (7 + 6a)) = 0 ((7 * 3 + 6a * 3) + 2a * (7 + 6a)) = 0 ((21 + 18a) + 2a * (7 + 6a)) = 0 (21 + 18a + (7 * 2a + 6a * 2a)) = 0 (21 + 18a + (14a + 12a2)) = 0 Combine like terms: 18a + 14a = 32a (21 + 32a + 12a2) = 0 Solving 21 + 32a + 12a2 = 0 Solving for variable 'a'. Factor a trinomial. (3 + 2a)(7 + 6a) = 0Subproblem 1
Set the factor '(3 + 2a)' equal to zero and attempt to solve: Simplifying 3 + 2a = 0 Solving 3 + 2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2a = 0 + -3 2a = 0 + -3 Combine like terms: 0 + -3 = -3 2a = -3 Divide each side by '2'. a = -1.5 Simplifying a = -1.5Subproblem 2
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 = -1.166666667Solution
a = {-1.5, -1.166666667}
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