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Simplifying -2(3v + -1w) + 5(2w + 2v) = 0 (3v * -2 + -1w * -2) + 5(2w + 2v) = 0 (-6v + 2w) + 5(2w + 2v) = 0 Reorder the terms: -6v + 2w + 5(2v + 2w) = 0 -6v + 2w + (2v * 5 + 2w * 5) = 0 -6v + 2w + (10v + 10w) = 0 Reorder the terms: -6v + 10v + 2w + 10w = 0 Combine like terms: -6v + 10v = 4v 4v + 2w + 10w = 0 Combine like terms: 2w + 10w = 12w 4v + 12w = 0 Solving 4v + 12w = 0 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-12w' to each side of the equation. 4v + 12w + -12w = 0 + -12w Combine like terms: 12w + -12w = 0 4v + 0 = 0 + -12w 4v = 0 + -12w Remove the zero: 4v = -12w Divide each side by '4'. v = -3w Simplifying v = -3w
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