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Simplifying 4u + 6v + -9(4u + -4v + 5w) = 0 4u + 6v + (4u * -9 + -4v * -9 + 5w * -9) = 0 4u + 6v + (-36u + 36v + -45w) = 0 Reorder the terms: 4u + -36u + 6v + 36v + -45w = 0 Combine like terms: 4u + -36u = -32u -32u + 6v + 36v + -45w = 0 Combine like terms: 6v + 36v = 42v -32u + 42v + -45w = 0 Solving -32u + 42v + -45w = 0 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-42v' to each side of the equation. -32u + 42v + -42v + -45w = 0 + -42v Combine like terms: 42v + -42v = 0 -32u + 0 + -45w = 0 + -42v -32u + -45w = 0 + -42v Remove the zero: -32u + -45w = -42v Add '45w' to each side of the equation. -32u + -45w + 45w = -42v + 45w Combine like terms: -45w + 45w = 0 -32u + 0 = -42v + 45w -32u = -42v + 45w Divide each side by '-32'. u = 1.3125v + -1.40625w Simplifying u = 1.3125v + -1.40625w
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