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Simplifying (4a + 3)(4a + 3) + -9 = 0 Reorder the terms: (3 + 4a)(4a + 3) + -9 = 0 Reorder the terms: (3 + 4a)(3 + 4a) + -9 = 0 Multiply (3 + 4a) * (3 + 4a) (3(3 + 4a) + 4a * (3 + 4a)) + -9 = 0 ((3 * 3 + 4a * 3) + 4a * (3 + 4a)) + -9 = 0 ((9 + 12a) + 4a * (3 + 4a)) + -9 = 0 (9 + 12a + (3 * 4a + 4a * 4a)) + -9 = 0 (9 + 12a + (12a + 16a2)) + -9 = 0 Combine like terms: 12a + 12a = 24a (9 + 24a + 16a2) + -9 = 0 Reorder the terms: 9 + -9 + 24a + 16a2 = 0 Combine like terms: 9 + -9 = 0 0 + 24a + 16a2 = 0 24a + 16a2 = 0 Solving 24a + 16a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '8a'. 8a(3 + 2a) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
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 = -1.5Solution
a = {0, -1.5}
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