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Simplifying 2(3v + 4w) + -3(4v + -4w) = 0 (3v * 2 + 4w * 2) + -3(4v + -4w) = 0 (6v + 8w) + -3(4v + -4w) = 0 6v + 8w + (4v * -3 + -4w * -3) = 0 6v + 8w + (-12v + 12w) = 0 Reorder the terms: 6v + -12v + 8w + 12w = 0 Combine like terms: 6v + -12v = -6v -6v + 8w + 12w = 0 Combine like terms: 8w + 12w = 20w -6v + 20w = 0 Solving -6v + 20w = 0 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-20w' to each side of the equation. -6v + 20w + -20w = 0 + -20w Combine like terms: 20w + -20w = 0 -6v + 0 = 0 + -20w -6v = 0 + -20w Remove the zero: -6v = -20w Divide each side by '-6'. v = 3.333333333w Simplifying v = 3.333333333w
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