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Simplifying 2((-3c + 4d) + -1(5d + -1c)) + -3(3c + -2d) = 0 Remove parenthesis around (-3c + 4d) 2(-3c + 4d + -1(5d + -1c)) + -3(3c + -2d) = 0 Reorder the terms: 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) = 0 Reorder the terms: 2(-3c + 1c + 4d + -5d) + -3(3c + -2d) = 0 Combine like terms: -3c + 1c = -2c 2(-2c + 4d + -5d) + -3(3c + -2d) = 0 Combine like terms: 4d + -5d = -1d 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) = 0 Reorder the terms: -4c + -9c + -2d + 6d = 0 Combine like terms: -4c + -9c = -13c -13c + -2d + 6d = 0 Combine like terms: -2d + 6d = 4d -13c + 4d = 0 Solving -13c + 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. -13c + 4d + -4d = 0 + -4d Combine like terms: 4d + -4d = 0 -13c + 0 = 0 + -4d -13c = 0 + -4d Remove the zero: -13c = -4d Divide each side by '-13'. c = 0.3076923077d Simplifying c = 0.3076923077d
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