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Simplifying (8a + 4)(9a + -2) = 0 Reorder the terms: (4 + 8a)(9a + -2) = 0 Reorder the terms: (4 + 8a)(-2 + 9a) = 0 Multiply (4 + 8a) * (-2 + 9a) (4(-2 + 9a) + 8a * (-2 + 9a)) = 0 ((-2 * 4 + 9a * 4) + 8a * (-2 + 9a)) = 0 ((-8 + 36a) + 8a * (-2 + 9a)) = 0 (-8 + 36a + (-2 * 8a + 9a * 8a)) = 0 (-8 + 36a + (-16a + 72a2)) = 0 Combine like terms: 36a + -16a = 20a (-8 + 20a + 72a2) = 0 Solving -8 + 20a + 72a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + 5a + 18a2) = 0 Factor a trinomial. 4((-1 + -2a)(2 + -9a)) = 0 Ignore the factor 4.Subproblem 1
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 = -0.5Subproblem 2
Set the factor '(2 + -9a)' equal to zero and attempt to solve: Simplifying 2 + -9a = 0 Solving 2 + -9a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -9a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9a = 0 + -2 -9a = 0 + -2 Combine like terms: 0 + -2 = -2 -9a = -2 Divide each side by '-9'. a = 0.2222222222 Simplifying a = 0.2222222222Solution
a = {-0.5, 0.2222222222}
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