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Simplifying (3q + -1p)(q + -1p)(p + 2q)(p + 4q) = 0 Reorder the terms: (-1p + 3q)(q + -1p)(p + 2q)(p + 4q) = 0 Reorder the terms: (-1p + 3q)(-1p + q)(p + 2q)(p + 4q) = 0 Multiply (-1p + 3q) * (-1p + q) (-1p * (-1p + q) + 3q * (-1p + q))(p + 2q)(p + 4q) = 0 ((-1p * -1p + q * -1p) + 3q * (-1p + q))(p + 2q)(p + 4q) = 0 Reorder the terms: ((-1pq + 1p2) + 3q * (-1p + q))(p + 2q)(p + 4q) = 0 ((-1pq + 1p2) + 3q * (-1p + q))(p + 2q)(p + 4q) = 0 (-1pq + 1p2 + (-1p * 3q + q * 3q))(p + 2q)(p + 4q) = 0 (-1pq + 1p2 + (-3pq + 3q2))(p + 2q)(p + 4q) = 0 Reorder the terms: (-1pq + -3pq + 1p2 + 3q2)(p + 2q)(p + 4q) = 0 Combine like terms: -1pq + -3pq = -4pq (-4pq + 1p2 + 3q2)(p + 2q)(p + 4q) = 0 Multiply (-4pq + 1p2 + 3q2) * (p + 2q) (-4pq * (p + 2q) + 1p2 * (p + 2q) + 3q2 * (p + 2q))(p + 4q) = 0 ((p * -4pq + 2q * -4pq) + 1p2 * (p + 2q) + 3q2 * (p + 2q))(p + 4q) = 0 Reorder the terms: ((-8pq2 + -4p2q) + 1p2 * (p + 2q) + 3q2 * (p + 2q))(p + 4q) = 0 ((-8pq2 + -4p2q) + 1p2 * (p + 2q) + 3q2 * (p + 2q))(p + 4q) = 0 (-8pq2 + -4p2q + (p * 1p2 + 2q * 1p2) + 3q2 * (p + 2q))(p + 4q) = 0 Reorder the terms: (-8pq2 + -4p2q + (2p2q + 1p3) + 3q2 * (p + 2q))(p + 4q) = 0 (-8pq2 + -4p2q + (2p2q + 1p3) + 3q2 * (p + 2q))(p + 4q) = 0 (-8pq2 + -4p2q + 2p2q + 1p3 + (p * 3q2 + 2q * 3q2))(p + 4q) = 0 (-8pq2 + -4p2q + 2p2q + 1p3 + (3pq2 + 6q3))(p + 4q) = 0 Reorder the terms: (-8pq2 + 3pq2 + -4p2q + 2p2q + 1p3 + 6q3)(p + 4q) = 0 Combine like terms: -8pq2 + 3pq2 = -5pq2 (-5pq2 + -4p2q + 2p2q + 1p3 + 6q3)(p + 4q) = 0 Combine like terms: -4p2q + 2p2q = -2p2q (-5pq2 + -2p2q + 1p3 + 6q3)(p + 4q) = 0 Multiply (-5pq2 + -2p2q + 1p3 + 6q3) * (p + 4q) (-5pq2 * (p + 4q) + -2p2q * (p + 4q) + 1p3 * (p + 4q) + 6q3 * (p + 4q)) = 0 ((p * -5pq2 + 4q * -5pq2) + -2p2q * (p + 4q) + 1p3 * (p + 4q) + 6q3 * (p + 4q)) = 0 Reorder the terms: ((-20pq3 + -5p2q2) + -2p2q * (p + 4q) + 1p3 * (p + 4q) + 6q3 * (p + 4q)) = 0 ((-20pq3 + -5p2q2) + -2p2q * (p + 4q) + 1p3 * (p + 4q) + 6q3 * (p + 4q)) = 0 (-20pq3 + -5p2q2 + (p * -2p2q + 4q * -2p2q) + 1p3 * (p + 4q) + 6q3 * (p + 4q)) = 0 Reorder the terms: (-20pq3 + -5p2q2 + (-8p2q2 + -2p3q) + 1p3 * (p + 4q) + 6q3 * (p + 4q)) = 0 (-20pq3 + -5p2q2 + (-8p2q2 + -2p3q) + 1p3 * (p + 4q) + 6q3 * (p + 4q)) = 0 (-20pq3 + -5p2q2 + -8p2q2 + -2p3q + (p * 1p3 + 4q * 1p3) + 6q3 * (p + 4q)) = 0 Reorder the terms: (-20pq3 + -5p2q2 + -8p2q2 + -2p3q + (4p3q + 1p4) + 6q3 * (p + 4q)) = 0 (-20pq3 + -5p2q2 + -8p2q2 + -2p3q + (4p3q + 1p4) + 6q3 * (p + 4q)) = 0 (-20pq3 + -5p2q2 + -8p2q2 + -2p3q + 4p3q + 1p4 + (p * 6q3 + 4q * 6q3)) = 0 (-20pq3 + -5p2q2 + -8p2q2 + -2p3q + 4p3q + 1p4 + (6pq3 + 24q4)) = 0 Reorder the terms: (-20pq3 + 6pq3 + -5p2q2 + -8p2q2 + -2p3q + 4p3q + 1p4 + 24q4) = 0 Combine like terms: -20pq3 + 6pq3 = -14pq3 (-14pq3 + -5p2q2 + -8p2q2 + -2p3q + 4p3q + 1p4 + 24q4) = 0 Combine like terms: -5p2q2 + -8p2q2 = -13p2q2 (-14pq3 + -13p2q2 + -2p3q + 4p3q + 1p4 + 24q4) = 0 Combine like terms: -2p3q + 4p3q = 2p3q (-14pq3 + -13p2q2 + 2p3q + 1p4 + 24q4) = 0 Solving -14pq3 + -13p2q2 + 2p3q + 1p4 + 24q4 = 0 Solving for variable 'p'. The solution to this equation could not be determined.
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