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Simplifying 7u + 3v + -7(7u + -6v + 3w) = 0 7u + 3v + (7u * -7 + -6v * -7 + 3w * -7) = 0 7u + 3v + (-49u + 42v + -21w) = 0 Reorder the terms: 7u + -49u + 3v + 42v + -21w = 0 Combine like terms: 7u + -49u = -42u -42u + 3v + 42v + -21w = 0 Combine like terms: 3v + 42v = 45v -42u + 45v + -21w = 0 Solving -42u + 45v + -21w = 0 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-45v' to each side of the equation. -42u + 45v + -45v + -21w = 0 + -45v Combine like terms: 45v + -45v = 0 -42u + 0 + -21w = 0 + -45v -42u + -21w = 0 + -45v Remove the zero: -42u + -21w = -45v Add '21w' to each side of the equation. -42u + -21w + 21w = -45v + 21w Combine like terms: -21w + 21w = 0 -42u + 0 = -45v + 21w -42u = -45v + 21w Divide each side by '-42'. u = 1.071428571v + -0.5w Simplifying u = 1.071428571v + -0.5w
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