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Simplifying (2a + -5)(6a + 2) = 0 Reorder the terms: (-5 + 2a)(6a + 2) = 0 Reorder the terms: (-5 + 2a)(2 + 6a) = 0 Multiply (-5 + 2a) * (2 + 6a) (-5(2 + 6a) + 2a * (2 + 6a)) = 0 ((2 * -5 + 6a * -5) + 2a * (2 + 6a)) = 0 ((-10 + -30a) + 2a * (2 + 6a)) = 0 (-10 + -30a + (2 * 2a + 6a * 2a)) = 0 (-10 + -30a + (4a + 12a2)) = 0 Combine like terms: -30a + 4a = -26a (-10 + -26a + 12a2) = 0 Solving -10 + -26a + 12a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -13a + 6a2) = 0 Factor a trinomial. 2((-1 + -3a)(5 + -2a)) = 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 + -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 = 2.5Solution
a = {-0.3333333333, 2.5}
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