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Simplifying 0 = 2[(-3c + 4d) + -1(5d + -1c)] + -3(3c + -2d) Remove parenthesis around (-3c + 4d) 0 = 2[-3c + 4d + -1(5d + -1c)] + -3(3c + -2d) Reorder the terms: 0 = 2[-3c + 4d + -1(-1c + 5d)] + -3(3c + -2d) 0 = 2[-3c + 4d + (-1c * -1 + 5d * -1)] + -3(3c + -2d) 0 = 2[-3c + 4d + (1c + -5d)] + -3(3c + -2d) Reorder the terms: 0 = 2[-3c + 1c + 4d + -5d] + -3(3c + -2d) Combine like terms: -3c + 1c = -2c 0 = 2[-2c + 4d + -5d] + -3(3c + -2d) Combine like terms: 4d + -5d = -1d 0 = 2[-2c + -1d] + -3(3c + -2d) 0 = [-2c * 2 + -1d * 2] + -3(3c + -2d) 0 = [-4c + -2d] + -3(3c + -2d) 0 = -4c + -2d + (3c * -3 + -2d * -3) 0 = -4c + -2d + (-9c + 6d) Reorder the terms: 0 = -4c + -9c + -2d + 6d Combine like terms: -4c + -9c = -13c 0 = -13c + -2d + 6d Combine like terms: -2d + 6d = 4d 0 = -13c + 4d Solving 0 = -13c + 4d Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '13c' to each side of the equation. 0 + 13c = -13c + 13c + 4d Remove the zero: 13c = -13c + 13c + 4d Combine like terms: -13c + 13c = 0 13c = 0 + 4d 13c = 4d Divide each side by '13'. c = 0.3076923077d Simplifying c = 0.3076923077d
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