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Simplifying (8a + -5)(9a + -6a + 9) = 0 Reorder the terms: (-5 + 8a)(9a + -6a + 9) = 0 Reorder the terms: (-5 + 8a)(9 + 9a + -6a) = 0 Combine like terms: 9a + -6a = 3a (-5 + 8a)(9 + 3a) = 0 Multiply (-5 + 8a) * (9 + 3a) (-5(9 + 3a) + 8a * (9 + 3a)) = 0 ((9 * -5 + 3a * -5) + 8a * (9 + 3a)) = 0 ((-45 + -15a) + 8a * (9 + 3a)) = 0 (-45 + -15a + (9 * 8a + 3a * 8a)) = 0 (-45 + -15a + (72a + 24a2)) = 0 Combine like terms: -15a + 72a = 57a (-45 + 57a + 24a2) = 0 Solving -45 + 57a + 24a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 19a + 8a2) = 0 Factor a trinomial. 3((-3 + -1a)(5 + -8a)) = 0 Ignore the factor 3.Subproblem 1
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 = -3Subproblem 2
Set the factor '(5 + -8a)' equal to zero and attempt to solve: Simplifying 5 + -8a = 0 Solving 5 + -8a = 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 + -8a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8a = 0 + -5 -8a = 0 + -5 Combine like terms: 0 + -5 = -5 -8a = -5 Divide each side by '-8'. a = 0.625 Simplifying a = 0.625Solution
a = {-3, 0.625}
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