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Simplifying (5a + -3)(6a + -5) = 0 Reorder the terms: (-3 + 5a)(6a + -5) = 0 Reorder the terms: (-3 + 5a)(-5 + 6a) = 0 Multiply (-3 + 5a) * (-5 + 6a) (-3(-5 + 6a) + 5a * (-5 + 6a)) = 0 ((-5 * -3 + 6a * -3) + 5a * (-5 + 6a)) = 0 ((15 + -18a) + 5a * (-5 + 6a)) = 0 (15 + -18a + (-5 * 5a + 6a * 5a)) = 0 (15 + -18a + (-25a + 30a2)) = 0 Combine like terms: -18a + -25a = -43a (15 + -43a + 30a2) = 0 Solving 15 + -43a + 30a2 = 0 Solving for variable 'a'. Factor a trinomial. (3 + -5a)(5 + -6a) = 0Subproblem 1
Set the factor '(3 + -5a)' equal to zero and attempt to solve: Simplifying 3 + -5a = 0 Solving 3 + -5a = 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 + -5a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5a = 0 + -3 -5a = 0 + -3 Combine like terms: 0 + -3 = -3 -5a = -3 Divide each side by '-5'. a = 0.6 Simplifying a = 0.6Subproblem 2
Set the factor '(5 + -6a)' equal to zero and attempt to solve: Simplifying 5 + -6a = 0 Solving 5 + -6a = 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 + -6a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6a = 0 + -5 -6a = 0 + -5 Combine like terms: 0 + -5 = -5 -6a = -5 Divide each side by '-6'. a = 0.8333333333 Simplifying a = 0.8333333333Solution
a = {0.6, 0.8333333333}
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