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Simplifying (5a + -7)(2a + -1) = 0 Reorder the terms: (-7 + 5a)(2a + -1) = 0 Reorder the terms: (-7 + 5a)(-1 + 2a) = 0 Multiply (-7 + 5a) * (-1 + 2a) (-7(-1 + 2a) + 5a * (-1 + 2a)) = 0 ((-1 * -7 + 2a * -7) + 5a * (-1 + 2a)) = 0 ((7 + -14a) + 5a * (-1 + 2a)) = 0 (7 + -14a + (-1 * 5a + 2a * 5a)) = 0 (7 + -14a + (-5a + 10a2)) = 0 Combine like terms: -14a + -5a = -19a (7 + -19a + 10a2) = 0 Solving 7 + -19a + 10a2 = 0 Solving for variable 'a'. Factor a trinomial. (1 + -2a)(7 + -5a) = 0Subproblem 1
Set the factor '(1 + -2a)' equal to zero and attempt to solve: Simplifying 1 + -2a = 0 Solving 1 + -2a = 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 + -2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a = 0 + -1 -2a = 0 + -1 Combine like terms: 0 + -1 = -1 -2a = -1 Divide each side by '-2'. a = 0.5 Simplifying a = 0.5Subproblem 2
Set the factor '(7 + -5a)' equal to zero and attempt to solve: Simplifying 7 + -5a = 0 Solving 7 + -5a = 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 + -5a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5a = 0 + -7 -5a = 0 + -7 Combine like terms: 0 + -7 = -7 -5a = -7 Divide each side by '-5'. a = 1.4 Simplifying a = 1.4Solution
a = {0.5, 1.4}
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