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Simplifying 4d + 2c + 4d + -1(d + -5) + 3(c + 2d) + 3c = 0 Reorder the terms: 4d + 2c + 4d + -1(-5 + d) + 3(c + 2d) + 3c = 0 4d + 2c + 4d + (-5 * -1 + d * -1) + 3(c + 2d) + 3c = 0 4d + 2c + 4d + (5 + -1d) + 3(c + 2d) + 3c = 0 4d + 2c + 4d + 5 + -1d + (c * 3 + 2d * 3) + 3c = 0 4d + 2c + 4d + 5 + -1d + (3c + 6d) + 3c = 0 Reorder the terms: 5 + 2c + 3c + 3c + 4d + 4d + -1d + 6d = 0 Combine like terms: 2c + 3c = 5c 5 + 5c + 3c + 4d + 4d + -1d + 6d = 0 Combine like terms: 5c + 3c = 8c 5 + 8c + 4d + 4d + -1d + 6d = 0 Combine like terms: 4d + 4d = 8d 5 + 8c + 8d + -1d + 6d = 0 Combine like terms: 8d + -1d = 7d 5 + 8c + 7d + 6d = 0 Combine like terms: 7d + 6d = 13d 5 + 8c + 13d = 0 Solving 5 + 8c + 13d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + 8c + -5 + 13d = 0 + -5 Reorder the terms: 5 + -5 + 8c + 13d = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8c + 13d = 0 + -5 8c + 13d = 0 + -5 Combine like terms: 0 + -5 = -5 8c + 13d = -5 Add '-13d' to each side of the equation. 8c + 13d + -13d = -5 + -13d Combine like terms: 13d + -13d = 0 8c + 0 = -5 + -13d 8c = -5 + -13d Divide each side by '8'. c = -0.625 + -1.625d Simplifying c = -0.625 + -1.625d
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