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Simplifying (3a + -5)(a + 2) = 0 Reorder the terms: (-5 + 3a)(a + 2) = 0 Reorder the terms: (-5 + 3a)(2 + a) = 0 Multiply (-5 + 3a) * (2 + a) (-5(2 + a) + 3a * (2 + a)) = 0 ((2 * -5 + a * -5) + 3a * (2 + a)) = 0 ((-10 + -5a) + 3a * (2 + a)) = 0 (-10 + -5a + (2 * 3a + a * 3a)) = 0 (-10 + -5a + (6a + 3a2)) = 0 Combine like terms: -5a + 6a = 1a (-10 + 1a + 3a2) = 0 Solving -10 + 1a + 3a2 = 0 Solving for variable 'a'. Factor a trinomial. (-2 + -1a)(5 + -3a) = 0Subproblem 1
Set the factor '(-2 + -1a)' equal to zero and attempt to solve: Simplifying -2 + -1a = 0 Solving -2 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1a = 0 + 2 -1a = 0 + 2 Combine like terms: 0 + 2 = 2 -1a = 2 Divide each side by '-1'. a = -2 Simplifying a = -2Subproblem 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 = {-2, 1.666666667}
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