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Simplifying (4a + 1)(a + 1) = (6 + -1a)(3a + -1) Reorder the terms: (1 + 4a)(a + 1) = (6 + -1a)(3a + -1) Reorder the terms: (1 + 4a)(1 + a) = (6 + -1a)(3a + -1) Multiply (1 + 4a) * (1 + a) (1(1 + a) + 4a * (1 + a)) = (6 + -1a)(3a + -1) ((1 * 1 + a * 1) + 4a * (1 + a)) = (6 + -1a)(3a + -1) ((1 + 1a) + 4a * (1 + a)) = (6 + -1a)(3a + -1) (1 + 1a + (1 * 4a + a * 4a)) = (6 + -1a)(3a + -1) (1 + 1a + (4a + 4a2)) = (6 + -1a)(3a + -1) Combine like terms: 1a + 4a = 5a (1 + 5a + 4a2) = (6 + -1a)(3a + -1) Reorder the terms: 1 + 5a + 4a2 = (6 + -1a)(-1 + 3a) Multiply (6 + -1a) * (-1 + 3a) 1 + 5a + 4a2 = (6(-1 + 3a) + -1a * (-1 + 3a)) 1 + 5a + 4a2 = ((-1 * 6 + 3a * 6) + -1a * (-1 + 3a)) 1 + 5a + 4a2 = ((-6 + 18a) + -1a * (-1 + 3a)) 1 + 5a + 4a2 = (-6 + 18a + (-1 * -1a + 3a * -1a)) 1 + 5a + 4a2 = (-6 + 18a + (1a + -3a2)) Combine like terms: 18a + 1a = 19a 1 + 5a + 4a2 = (-6 + 19a + -3a2) Solving 1 + 5a + 4a2 = -6 + 19a + -3a2 Solving for variable 'a'. Reorder the terms: 1 + 6 + 5a + -19a + 4a2 + 3a2 = -6 + 19a + -3a2 + 6 + -19a + 3a2 Combine like terms: 1 + 6 = 7 7 + 5a + -19a + 4a2 + 3a2 = -6 + 19a + -3a2 + 6 + -19a + 3a2 Combine like terms: 5a + -19a = -14a 7 + -14a + 4a2 + 3a2 = -6 + 19a + -3a2 + 6 + -19a + 3a2 Combine like terms: 4a2 + 3a2 = 7a2 7 + -14a + 7a2 = -6 + 19a + -3a2 + 6 + -19a + 3a2 Reorder the terms: 7 + -14a + 7a2 = -6 + 6 + 19a + -19a + -3a2 + 3a2 Combine like terms: -6 + 6 = 0 7 + -14a + 7a2 = 0 + 19a + -19a + -3a2 + 3a2 7 + -14a + 7a2 = 19a + -19a + -3a2 + 3a2 Combine like terms: 19a + -19a = 0 7 + -14a + 7a2 = 0 + -3a2 + 3a2 7 + -14a + 7a2 = -3a2 + 3a2 Combine like terms: -3a2 + 3a2 = 0 7 + -14a + 7a2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(1 + -2a + a2) = 0 Factor a trinomial. 7((1 + -1a)(1 + -1a)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(1 + -1a)' equal to zero and attempt to solve: Simplifying 1 + -1a = 0 Solving 1 + -1a = 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 + -1a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a = 0 + -1 -1a = 0 + -1 Combine like terms: 0 + -1 = -1 -1a = -1 Divide each side by '-1'. a = 1 Simplifying a = 1Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve: Simplifying 1 + -1a = 0 Solving 1 + -1a = 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 + -1a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a = 0 + -1 -1a = 0 + -1 Combine like terms: 0 + -1 = -1 -1a = -1 Divide each side by '-1'. a = 1 Simplifying a = 1Solution
a = {1, 1}
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