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Simplifying 6 + -1(2c + -1) = (3 + 2c)(3 + -2c) Reorder the terms: 6 + -1(-1 + 2c) = (3 + 2c)(3 + -2c) 6 + (-1 * -1 + 2c * -1) = (3 + 2c)(3 + -2c) 6 + (1 + -2c) = (3 + 2c)(3 + -2c) Combine like terms: 6 + 1 = 7 7 + -2c = (3 + 2c)(3 + -2c) Multiply (3 + 2c) * (3 + -2c) 7 + -2c = (3(3 + -2c) + 2c * (3 + -2c)) 7 + -2c = ((3 * 3 + -2c * 3) + 2c * (3 + -2c)) 7 + -2c = ((9 + -6c) + 2c * (3 + -2c)) 7 + -2c = (9 + -6c + (3 * 2c + -2c * 2c)) 7 + -2c = (9 + -6c + (6c + -4c2)) Combine like terms: -6c + 6c = 0 7 + -2c = (9 + 0 + -4c2) 7 + -2c = (9 + -4c2) Solving 7 + -2c = 9 + -4c2 Solving for variable 'c'. Reorder the terms: 7 + -9 + -2c + 4c2 = 9 + -4c2 + -9 + 4c2 Combine like terms: 7 + -9 = -2 -2 + -2c + 4c2 = 9 + -4c2 + -9 + 4c2 Reorder the terms: -2 + -2c + 4c2 = 9 + -9 + -4c2 + 4c2 Combine like terms: 9 + -9 = 0 -2 + -2c + 4c2 = 0 + -4c2 + 4c2 -2 + -2c + 4c2 = -4c2 + 4c2 Combine like terms: -4c2 + 4c2 = 0 -2 + -2c + 4c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -1c + 2c2) = 0 Factor a trinomial. 2((-1 + -2c)(1 + -1c)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -2c)' equal to zero and attempt to solve: Simplifying -1 + -2c = 0 Solving -1 + -2c = 0 Move all terms containing c to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2c = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2c = 0 + 1 -2c = 0 + 1 Combine like terms: 0 + 1 = 1 -2c = 1 Divide each side by '-2'. c = -0.5 Simplifying c = -0.5Subproblem 2
Set the factor '(1 + -1c)' equal to zero and attempt to solve: Simplifying 1 + -1c = 0 Solving 1 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1c = 0 + -1 -1c = 0 + -1 Combine like terms: 0 + -1 = -1 -1c = -1 Divide each side by '-1'. c = 1 Simplifying c = 1Solution
c = {-0.5, 1}
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