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Simplifying (3a + -5)(2a + -1) = 0 Reorder the terms: (-5 + 3a)(2a + -1) = 0 Reorder the terms: (-5 + 3a)(-1 + 2a) = 0 Multiply (-5 + 3a) * (-1 + 2a) (-5(-1 + 2a) + 3a * (-1 + 2a)) = 0 ((-1 * -5 + 2a * -5) + 3a * (-1 + 2a)) = 0 ((5 + -10a) + 3a * (-1 + 2a)) = 0 (5 + -10a + (-1 * 3a + 2a * 3a)) = 0 (5 + -10a + (-3a + 6a2)) = 0 Combine like terms: -10a + -3a = -13a (5 + -13a + 6a2) = 0 Solving 5 + -13a + 6a2 = 0 Solving for variable 'a'. Factor a trinomial. (1 + -2a)(5 + -3a) = 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 '(5 + -3a)' equal to zero and attempt to solve: Simplifying 5 + -3a = 0 Solving 5 + -3a = 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 + -3a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3a = 0 + -5 -3a = 0 + -5 Combine like terms: 0 + -5 = -5 -3a = -5 Divide each side by '-3'. a = 1.666666667 Simplifying a = 1.666666667Solution
a = {0.5, 1.666666667}
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