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Simplifying (3a + 5)(2a + -6) = 0 Reorder the terms: (5 + 3a)(2a + -6) = 0 Reorder the terms: (5 + 3a)(-6 + 2a) = 0 Multiply (5 + 3a) * (-6 + 2a) (5(-6 + 2a) + 3a * (-6 + 2a)) = 0 ((-6 * 5 + 2a * 5) + 3a * (-6 + 2a)) = 0 ((-30 + 10a) + 3a * (-6 + 2a)) = 0 (-30 + 10a + (-6 * 3a + 2a * 3a)) = 0 (-30 + 10a + (-18a + 6a2)) = 0 Combine like terms: 10a + -18a = -8a (-30 + -8a + 6a2) = 0 Solving -30 + -8a + 6a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -4a + 3a2) = 0 Factor a trinomial. 2((-5 + -3a)(3 + -1a)) = 0 Ignore the factor 2.Subproblem 1
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 = -1.666666667Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve: Simplifying 3 + -1a = 0 Solving 3 + -1a = 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 + -1a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1a = 0 + -3 -1a = 0 + -3 Combine like terms: 0 + -3 = -3 -1a = -3 Divide each side by '-1'. a = 3 Simplifying a = 3Solution
a = {-1.666666667, 3}
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