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Simplifying (6a + 2)(4a + -5) = 0 Reorder the terms: (2 + 6a)(4a + -5) = 0 Reorder the terms: (2 + 6a)(-5 + 4a) = 0 Multiply (2 + 6a) * (-5 + 4a) (2(-5 + 4a) + 6a * (-5 + 4a)) = 0 ((-5 * 2 + 4a * 2) + 6a * (-5 + 4a)) = 0 ((-10 + 8a) + 6a * (-5 + 4a)) = 0 (-10 + 8a + (-5 * 6a + 4a * 6a)) = 0 (-10 + 8a + (-30a + 24a2)) = 0 Combine like terms: 8a + -30a = -22a (-10 + -22a + 24a2) = 0 Solving -10 + -22a + 24a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -11a + 12a2) = 0 Factor a trinomial. 2((-1 + -3a)(5 + -4a)) = 0 Ignore the factor 2.Subproblem 1
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 = -0.3333333333Subproblem 2
Set the factor '(5 + -4a)' equal to zero and attempt to solve: Simplifying 5 + -4a = 0 Solving 5 + -4a = 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 + -4a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4a = 0 + -5 -4a = 0 + -5 Combine like terms: 0 + -5 = -5 -4a = -5 Divide each side by '-4'. a = 1.25 Simplifying a = 1.25Solution
a = {-0.3333333333, 1.25}
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