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Simplifying 3(3u + 2v) + -3(4u + -3v) = 0 (3u * 3 + 2v * 3) + -3(4u + -3v) = 0 (9u + 6v) + -3(4u + -3v) = 0 9u + 6v + (4u * -3 + -3v * -3) = 0 9u + 6v + (-12u + 9v) = 0 Reorder the terms: 9u + -12u + 6v + 9v = 0 Combine like terms: 9u + -12u = -3u -3u + 6v + 9v = 0 Combine like terms: 6v + 9v = 15v -3u + 15v = 0 Solving -3u + 15v = 0 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-15v' to each side of the equation. -3u + 15v + -15v = 0 + -15v Combine like terms: 15v + -15v = 0 -3u + 0 = 0 + -15v -3u = 0 + -15v Remove the zero: -3u = -15v Divide each side by '-3'. u = 5v Simplifying u = 5v
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