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Simplifying P(2n + m) + q(2m + n) = 0 Reorder the terms: P(m + 2n) + q(2m + n) = 0 (m * P + 2n * P) + q(2m + n) = 0 (mP + 2nP) + q(2m + n) = 0 mP + 2nP + (2m * q + n * q) = 0 mP + 2nP + (2mq + nq) = 0 Reorder the terms: mP + 2mq + 2nP + nq = 0 Solving mP + 2mq + 2nP + nq = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2nP' to each side of the equation. mP + 2mq + 2nP + -2nP + nq = 0 + -2nP Combine like terms: 2nP + -2nP = 0 mP + 2mq + 0 + nq = 0 + -2nP mP + 2mq + nq = 0 + -2nP Remove the zero: mP + 2mq + nq = -2nP Add '-1nq' to each side of the equation. mP + 2mq + nq + -1nq = -2nP + -1nq Combine like terms: nq + -1nq = 0 mP + 2mq + 0 = -2nP + -1nq mP + 2mq = -2nP + -1nq Reorder the terms: mP + 2mq + 2nP + nq = -2nP + 2nP + -1nq + nq Combine like terms: -2nP + 2nP = 0 mP + 2mq + 2nP + nq = 0 + -1nq + nq mP + 2mq + 2nP + nq = -1nq + nq Combine like terms: -1nq + nq = 0 mP + 2mq + 2nP + nq = 0 The solution to this equation could not be determined.
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