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Simplifying 6u + 3v + -9(6u + -6v + 3w) = 0 6u + 3v + (6u * -9 + -6v * -9 + 3w * -9) = 0 6u + 3v + (-54u + 54v + -27w) = 0 Reorder the terms: 6u + -54u + 3v + 54v + -27w = 0 Combine like terms: 6u + -54u = -48u -48u + 3v + 54v + -27w = 0 Combine like terms: 3v + 54v = 57v -48u + 57v + -27w = 0 Solving -48u + 57v + -27w = 0 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-57v' to each side of the equation. -48u + 57v + -57v + -27w = 0 + -57v Combine like terms: 57v + -57v = 0 -48u + 0 + -27w = 0 + -57v -48u + -27w = 0 + -57v Remove the zero: -48u + -27w = -57v Add '27w' to each side of the equation. -48u + -27w + 27w = -57v + 27w Combine like terms: -27w + 27w = 0 -48u + 0 = -57v + 27w -48u = -57v + 27w Divide each side by '-48'. u = 1.1875v + -0.5625w Simplifying u = 1.1875v + -0.5625w
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