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Simplifying (5a + -1)(7a + 5) = 0 Reorder the terms: (-1 + 5a)(7a + 5) = 0 Reorder the terms: (-1 + 5a)(5 + 7a) = 0 Multiply (-1 + 5a) * (5 + 7a) (-1(5 + 7a) + 5a * (5 + 7a)) = 0 ((5 * -1 + 7a * -1) + 5a * (5 + 7a)) = 0 ((-5 + -7a) + 5a * (5 + 7a)) = 0 (-5 + -7a + (5 * 5a + 7a * 5a)) = 0 (-5 + -7a + (25a + 35a2)) = 0 Combine like terms: -7a + 25a = 18a (-5 + 18a + 35a2) = 0 Solving -5 + 18a + 35a2 = 0 Solving for variable 'a'. Factor a trinomial. (-5 + -7a)(1 + -5a) = 0Subproblem 1
Set the factor '(-5 + -7a)' equal to zero and attempt to solve: Simplifying -5 + -7a = 0 Solving -5 + -7a = 0 Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -7a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -7a = 0 + 5 -7a = 0 + 5 Combine like terms: 0 + 5 = 5 -7a = 5 Divide each side by '-7'. a = -0.7142857143 Simplifying a = -0.7142857143Subproblem 2
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 = 0.2Solution
a = {-0.7142857143, 0.2}
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