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Simplifying 3(4v + 1) + -3(2v + 3) = 0 Reorder the terms: 3(1 + 4v) + -3(2v + 3) = 0 (1 * 3 + 4v * 3) + -3(2v + 3) = 0 (3 + 12v) + -3(2v + 3) = 0 Reorder the terms: 3 + 12v + -3(3 + 2v) = 0 3 + 12v + (3 * -3 + 2v * -3) = 0 3 + 12v + (-9 + -6v) = 0 Reorder the terms: 3 + -9 + 12v + -6v = 0 Combine like terms: 3 + -9 = -6 -6 + 12v + -6v = 0 Combine like terms: 12v + -6v = 6v -6 + 6v = 0 Solving -6 + 6v = 0 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + 6v = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 6v = 0 + 6 6v = 0 + 6 Combine like terms: 0 + 6 = 6 6v = 6 Divide each side by '6'. v = 1 Simplifying v = 1
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