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Simplifying (3a + -1)(2a + 5) = 0 Reorder the terms: (-1 + 3a)(2a + 5) = 0 Reorder the terms: (-1 + 3a)(5 + 2a) = 0 Multiply (-1 + 3a) * (5 + 2a) (-1(5 + 2a) + 3a * (5 + 2a)) = 0 ((5 * -1 + 2a * -1) + 3a * (5 + 2a)) = 0 ((-5 + -2a) + 3a * (5 + 2a)) = 0 (-5 + -2a + (5 * 3a + 2a * 3a)) = 0 (-5 + -2a + (15a + 6a2)) = 0 Combine like terms: -2a + 15a = 13a (-5 + 13a + 6a2) = 0 Solving -5 + 13a + 6a2 = 0 Solving for variable 'a'. Factor a trinomial. (-5 + -2a)(1 + -3a) = 0Subproblem 1
Set the factor '(-5 + -2a)' equal to zero and attempt to solve: Simplifying -5 + -2a = 0 Solving -5 + -2a = 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 + -2a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2a = 0 + 5 -2a = 0 + 5 Combine like terms: 0 + 5 = 5 -2a = 5 Divide each side by '-2'. a = -2.5 Simplifying a = -2.5Subproblem 2
Set the factor '(1 + -3a)' equal to zero and attempt to solve: Simplifying 1 + -3a = 0 Solving 1 + -3a = 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 + -3a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3a = 0 + -1 -3a = 0 + -1 Combine like terms: 0 + -1 = -1 -3a = -1 Divide each side by '-3'. a = 0.3333333333 Simplifying a = 0.3333333333Solution
a = {-2.5, 0.3333333333}
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