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Simplifying (2c) * mi + (2c + 1) * mi + (3c + 2) * mi + (4c + 2) * mi = 0 Remove parenthesis around (2c) 2c * mi + (2c + 1) * mi + (3c + 2) * mi + (4c + 2) * mi = 0 Multiply c * im 2cim + (2c + 1) * mi + (3c + 2) * mi + (4c + 2) * mi = 0 Reorder the terms: 2cim + (1 + 2c) * mi + (3c + 2) * mi + (4c + 2) * mi = 0 Reorder the terms for easier multiplication: 2cim + im(1 + 2c) + (3c + 2) * mi + (4c + 2) * mi = 0 2cim + (1 * im + 2c * im) + (3c + 2) * mi + (4c + 2) * mi = 0 Reorder the terms: 2cim + (2cim + 1im) + (3c + 2) * mi + (4c + 2) * mi = 0 2cim + (2cim + 1im) + (3c + 2) * mi + (4c + 2) * mi = 0 Reorder the terms: 2cim + 2cim + 1im + (2 + 3c) * mi + (4c + 2) * mi = 0 Reorder the terms for easier multiplication: 2cim + 2cim + 1im + im(2 + 3c) + (4c + 2) * mi = 0 2cim + 2cim + 1im + (2 * im + 3c * im) + (4c + 2) * mi = 0 Reorder the terms: 2cim + 2cim + 1im + (3cim + 2im) + (4c + 2) * mi = 0 2cim + 2cim + 1im + (3cim + 2im) + (4c + 2) * mi = 0 Reorder the terms: 2cim + 2cim + 1im + 3cim + 2im + (2 + 4c) * mi = 0 Reorder the terms for easier multiplication: 2cim + 2cim + 1im + 3cim + 2im + im(2 + 4c) = 0 2cim + 2cim + 1im + 3cim + 2im + (2 * im + 4c * im) = 0 Reorder the terms: 2cim + 2cim + 1im + 3cim + 2im + (4cim + 2im) = 0 2cim + 2cim + 1im + 3cim + 2im + (4cim + 2im) = 0 Reorder the terms: 2cim + 2cim + 3cim + 4cim + 1im + 2im + 2im = 0 Combine like terms: 2cim + 2cim = 4cim 4cim + 3cim + 4cim + 1im + 2im + 2im = 0 Combine like terms: 4cim + 3cim = 7cim 7cim + 4cim + 1im + 2im + 2im = 0 Combine like terms: 7cim + 4cim = 11cim 11cim + 1im + 2im + 2im = 0 Combine like terms: 1im + 2im = 3im 11cim + 3im + 2im = 0 Combine like terms: 3im + 2im = 5im 11cim + 5im = 0 Solving 11cim + 5im = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-5im' to each side of the equation. 11cim + 5im + -5im = 0 + -5im Combine like terms: 5im + -5im = 0 11cim + 0 = 0 + -5im 11cim = 0 + -5im Remove the zero: 11cim = -5im Divide each side by '11im'. c = -0.4545454545 Simplifying c = -0.4545454545
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