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Simplifying (5a + -12)(9 + 6a) = 0 Reorder the terms: (-12 + 5a)(9 + 6a) = 0 Multiply (-12 + 5a) * (9 + 6a) (-12(9 + 6a) + 5a * (9 + 6a)) = 0 ((9 * -12 + 6a * -12) + 5a * (9 + 6a)) = 0 ((-108 + -72a) + 5a * (9 + 6a)) = 0 (-108 + -72a + (9 * 5a + 6a * 5a)) = 0 (-108 + -72a + (45a + 30a2)) = 0 Combine like terms: -72a + 45a = -27a (-108 + -27a + 30a2) = 0 Solving -108 + -27a + 30a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(-36 + -9a + 10a2) = 0 Factor a trinomial. 3((-3 + -2a)(12 + -5a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -2a)' equal to zero and attempt to solve: Simplifying -3 + -2a = 0 Solving -3 + -2a = 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 + -2a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2a = 0 + 3 -2a = 0 + 3 Combine like terms: 0 + 3 = 3 -2a = 3 Divide each side by '-2'. a = -1.5 Simplifying a = -1.5Subproblem 2
Set the factor '(12 + -5a)' equal to zero and attempt to solve: Simplifying 12 + -5a = 0 Solving 12 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -5a = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -5a = 0 + -12 -5a = 0 + -12 Combine like terms: 0 + -12 = -12 -5a = -12 Divide each side by '-5'. a = 2.4 Simplifying a = 2.4Solution
a = {-1.5, 2.4}
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