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Simplifying -2(c + -1d) + (c + -3d) + -5(c + -1d) = 0 (c * -2 + -1d * -2) + (c + -3d) + -5(c + -1d) = 0 (-2c + 2d) + (c + -3d) + -5(c + -1d) = 0 Remove parenthesis around (c + -3d) -2c + 2d + c + -3d + -5(c + -1d) = 0 -2c + 2d + c + -3d + (c * -5 + -1d * -5) = 0 -2c + 2d + c + -3d + (-5c + 5d) = 0 Reorder the terms: -2c + c + -5c + 2d + -3d + 5d = 0 Combine like terms: -2c + c = -1c -1c + -5c + 2d + -3d + 5d = 0 Combine like terms: -1c + -5c = -6c -6c + 2d + -3d + 5d = 0 Combine like terms: 2d + -3d = -1d -6c + -1d + 5d = 0 Combine like terms: -1d + 5d = 4d -6c + 4d = 0 Solving -6c + 4d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4d' to each side of the equation. -6c + 4d + -4d = 0 + -4d Combine like terms: 4d + -4d = 0 -6c + 0 = 0 + -4d -6c = 0 + -4d Remove the zero: -6c = -4d Divide each side by '-6'. c = 0.6666666667d Simplifying c = 0.6666666667d
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