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Simplifying 2a + -2(2a + -1) + -2(a + -1)(2a + -1) = 0 Reorder the terms: 2a + -2(-1 + 2a) + -2(a + -1)(2a + -1) = 0 2a + (-1 * -2 + 2a * -2) + -2(a + -1)(2a + -1) = 0 2a + (2 + -4a) + -2(a + -1)(2a + -1) = 0 Reorder the terms: 2a + 2 + -4a + -2(-1 + a)(2a + -1) = 0 Reorder the terms: 2a + 2 + -4a + -2(-1 + a)(-1 + 2a) = 0 Multiply (-1 + a) * (-1 + 2a) 2a + 2 + -4a + -2(-1(-1 + 2a) + a(-1 + 2a)) = 0 2a + 2 + -4a + -2((-1 * -1 + 2a * -1) + a(-1 + 2a)) = 0 2a + 2 + -4a + -2((1 + -2a) + a(-1 + 2a)) = 0 2a + 2 + -4a + -2(1 + -2a + (-1 * a + 2a * a)) = 0 2a + 2 + -4a + -2(1 + -2a + (-1a + 2a2)) = 0 Combine like terms: -2a + -1a = -3a 2a + 2 + -4a + -2(1 + -3a + 2a2) = 0 2a + 2 + -4a + (1 * -2 + -3a * -2 + 2a2 * -2) = 0 2a + 2 + -4a + (-2 + 6a + -4a2) = 0 Reorder the terms: 2 + -2 + 2a + -4a + 6a + -4a2 = 0 Combine like terms: 2 + -2 = 0 0 + 2a + -4a + 6a + -4a2 = 0 2a + -4a + 6a + -4a2 = 0 Combine like terms: 2a + -4a = -2a -2a + 6a + -4a2 = 0 Combine like terms: -2a + 6a = 4a 4a + -4a2 = 0 Solving 4a + -4a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4a'. 4a(1 + -1a) = 0 Ignore the factor 4.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 '(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 = {0, 1}
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