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Simplifying 3(p + 2q) + 2(3p + q) = 0 (p * 3 + 2q * 3) + 2(3p + q) = 0 (3p + 6q) + 2(3p + q) = 0 3p + 6q + (3p * 2 + q * 2) = 0 3p + 6q + (6p + 2q) = 0 Reorder the terms: 3p + 6p + 6q + 2q = 0 Combine like terms: 3p + 6p = 9p 9p + 6q + 2q = 0 Combine like terms: 6q + 2q = 8q 9p + 8q = 0 Solving 9p + 8q = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-8q' to each side of the equation. 9p + 8q + -8q = 0 + -8q Combine like terms: 8q + -8q = 0 9p + 0 = 0 + -8q 9p = 0 + -8q Remove the zero: 9p = -8q Divide each side by '9'. p = -0.8888888889q Simplifying p = -0.8888888889q
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