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Simplifying (6a + 1)(5a + 2) = 0 Reorder the terms: (1 + 6a)(5a + 2) = 0 Reorder the terms: (1 + 6a)(2 + 5a) = 0 Multiply (1 + 6a) * (2 + 5a) (1(2 + 5a) + 6a * (2 + 5a)) = 0 ((2 * 1 + 5a * 1) + 6a * (2 + 5a)) = 0 ((2 + 5a) + 6a * (2 + 5a)) = 0 (2 + 5a + (2 * 6a + 5a * 6a)) = 0 (2 + 5a + (12a + 30a2)) = 0 Combine like terms: 5a + 12a = 17a (2 + 17a + 30a2) = 0 Solving 2 + 17a + 30a2 = 0 Solving for variable 'a'. Factor a trinomial. (2 + 5a)(1 + 6a) = 0Subproblem 1
Set the factor '(2 + 5a)' equal to zero and attempt to solve: Simplifying 2 + 5a = 0 Solving 2 + 5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5a = 0 + -2 5a = 0 + -2 Combine like terms: 0 + -2 = -2 5a = -2 Divide each side by '5'. a = -0.4 Simplifying a = -0.4Subproblem 2
Set the factor '(1 + 6a)' equal to zero and attempt to solve: Simplifying 1 + 6a = 0 Solving 1 + 6a = 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 + 6a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6a = 0 + -1 6a = 0 + -1 Combine like terms: 0 + -1 = -1 6a = -1 Divide each side by '6'. a = -0.1666666667 Simplifying a = -0.1666666667Solution
a = {-0.4, -0.1666666667}
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