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Simplifying (6a + -3)(8a + -3) = 0 Reorder the terms: (-3 + 6a)(8a + -3) = 0 Reorder the terms: (-3 + 6a)(-3 + 8a) = 0 Multiply (-3 + 6a) * (-3 + 8a) (-3(-3 + 8a) + 6a * (-3 + 8a)) = 0 ((-3 * -3 + 8a * -3) + 6a * (-3 + 8a)) = 0 ((9 + -24a) + 6a * (-3 + 8a)) = 0 (9 + -24a + (-3 * 6a + 8a * 6a)) = 0 (9 + -24a + (-18a + 48a2)) = 0 Combine like terms: -24a + -18a = -42a (9 + -42a + 48a2) = 0 Solving 9 + -42a + 48a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -14a + 16a2) = 0 Factor a trinomial. 3((3 + -8a)(1 + -2a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -8a)' equal to zero and attempt to solve: Simplifying 3 + -8a = 0 Solving 3 + -8a = 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 + -8a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8a = 0 + -3 -8a = 0 + -3 Combine like terms: 0 + -3 = -3 -8a = -3 Divide each side by '-8'. a = 0.375 Simplifying a = 0.375Subproblem 2
Set the factor '(1 + -2a)' equal to zero and attempt to solve: Simplifying 1 + -2a = 0 Solving 1 + -2a = 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 + -2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a = 0 + -1 -2a = 0 + -1 Combine like terms: 0 + -1 = -1 -2a = -1 Divide each side by '-2'. a = 0.5 Simplifying a = 0.5Solution
a = {0.375, 0.5}
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