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Simplifying (5a + -1)(6a + -7) = 0 Reorder the terms: (-1 + 5a)(6a + -7) = 0 Reorder the terms: (-1 + 5a)(-7 + 6a) = 0 Multiply (-1 + 5a) * (-7 + 6a) (-1(-7 + 6a) + 5a * (-7 + 6a)) = 0 ((-7 * -1 + 6a * -1) + 5a * (-7 + 6a)) = 0 ((7 + -6a) + 5a * (-7 + 6a)) = 0 (7 + -6a + (-7 * 5a + 6a * 5a)) = 0 (7 + -6a + (-35a + 30a2)) = 0 Combine like terms: -6a + -35a = -41a (7 + -41a + 30a2) = 0 Solving 7 + -41a + 30a2 = 0 Solving for variable 'a'. Factor a trinomial. (1 + -5a)(7 + -6a) = 0Subproblem 1
Set the factor '(1 + -5a)' equal to zero and attempt to solve: Simplifying 1 + -5a = 0 Solving 1 + -5a = 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 + -5a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5a = 0 + -1 -5a = 0 + -1 Combine like terms: 0 + -1 = -1 -5a = -1 Divide each side by '-5'. a = 0.2 Simplifying a = 0.2Subproblem 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 = {0.2, 1.166666667}
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