(p^2-q+r)(q^2-p+r)(p+q-r)=

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Solution for (p^2-q+r)(q^2-p+r)(p+q-r)= equation: 


Simplifying
(p2 + -1q + r)(q2 + -1p + r)(p + q + -1r) = 0

Reorder the terms:
(p2 + -1q + r)(-1p + q2 + r)(p + q + -1r) = 0

Multiply (p2 + -1q + r) * (-1p + q2 + r)
(p2(-1p + q2 + r) + -1q * (-1p + q2 + r) + r(-1p + q2 + r))(p + q + -1r) = 0
((-1p * p2 + q2 * p2 + r * p2) + -1q * (-1p + q2 + r) + r(-1p + q2 + r))(p + q + -1r) = 0

Reorder the terms:
((p2q2 + p2r + -1p3) + -1q * (-1p + q2 + r) + r(-1p + q2 + r))(p + q + -1r) = 0
((p2q2 + p2r + -1p3) + -1q * (-1p + q2 + r) + r(-1p + q2 + r))(p + q + -1r) = 0
(p2q2 + p2r + -1p3 + (-1p * -1q + q2 * -1q + r * -1q) + r(-1p + q2 + r))(p + q + -1r) = 0

Reorder the terms:
(p2q2 + p2r + -1p3 + (1pq + -1qr + -1q3) + r(-1p + q2 + r))(p + q + -1r) = 0
(p2q2 + p2r + -1p3 + (1pq + -1qr + -1q3) + r(-1p + q2 + r))(p + q + -1r) = 0
(p2q2 + p2r + -1p3 + 1pq + -1qr + -1q3 + (-1p * r + q2 * r + r * r))(p + q + -1r) = 0
(p2q2 + p2r + -1p3 + 1pq + -1qr + -1q3 + (-1pr + q2r + r2))(p + q + -1r) = 0

Reorder the terms:
(1pq + -1pr + p2q2 + p2r + -1p3 + -1qr + q2r + -1q3 + r2)(p + q + -1r) = 0
(1pq + -1pr + p2q2 + p2r + -1p3 + -1qr + q2r + -1q3 + r2)(p + q + -1r) = 0

Multiply (1pq + -1pr + p2q2 + p2r + -1p3 + -1qr + q2r + -1q3 + r2) * (p + q + -1r)
(1pq * (p + q + -1r) + -1pr * (p + q + -1r) + p2q2(p + q + -1r) + p2r(p + q + -1r) + -1p3 * (p + q + -1r) + -1qr * (p + q + -1r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0
((p * 1pq + q * 1pq + -1r * 1pq) + -1pr * (p + q + -1r) + p2q2(p + q + -1r) + p2r(p + q + -1r) + -1p3 * (p + q + -1r) + -1qr * (p + q + -1r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0

Reorder the terms:
((-1pqr + 1pq2 + 1p2q) + -1pr * (p + q + -1r) + p2q2(p + q + -1r) + p2r(p + q + -1r) + -1p3 * (p + q + -1r) + -1qr * (p + q + -1r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0
((-1pqr + 1pq2 + 1p2q) + -1pr * (p + q + -1r) + p2q2(p + q + -1r) + p2r(p + q + -1r) + -1p3 * (p + q + -1r) + -1qr * (p + q + -1r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0
(-1pqr + 1pq2 + 1p2q + (p * -1pr + q * -1pr + -1r * -1pr) + p2q2(p + q + -1r) + p2r(p + q + -1r) + -1p3 * (p + q + -1r) + -1qr * (p + q + -1r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0

Reorder the terms:
(-1pqr + 1pq2 + 1p2q + (-1pqr + 1pr2 + -1p2r) + p2q2(p + q + -1r) + p2r(p + q + -1r) + -1p3 * (p + q + -1r) + -1qr * (p + q + -1r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0
(-1pqr + 1pq2 + 1p2q + (-1pqr + 1pr2 + -1p2r) + p2q2(p + q + -1r) + p2r(p + q + -1r) + -1p3 * (p + q + -1r) + -1qr * (p + q + -1r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + (p * p2q2 + q * p2q2 + -1r * p2q2) + p2r(p + q + -1r) + -1p3 * (p + q + -1r) + -1qr * (p + q + -1r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0

Reorder the terms:
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + (-1p2q2r + p2q3 + p3q2) + p2r(p + q + -1r) + -1p3 * (p + q + -1r) + -1qr * (p + q + -1r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + (-1p2q2r + p2q3 + p3q2) + p2r(p + q + -1r) + -1p3 * (p + q + -1r) + -1qr * (p + q + -1r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + -1p2q2r + p2q3 + p3q2 + (p * p2r + q * p2r + -1r * p2r) + -1p3 * (p + q + -1r) + -1qr * (p + q + -1r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0

Reorder the terms:
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + -1p2q2r + p2q3 + p3q2 + (p2qr + -1p2r2 + p3r) + -1p3 * (p + q + -1r) + -1qr * (p + q + -1r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + -1p2q2r + p2q3 + p3q2 + (p2qr + -1p2r2 + p3r) + -1p3 * (p + q + -1r) + -1qr * (p + q + -1r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + -1p2q2r + p2q3 + p3q2 + p2qr + -1p2r2 + p3r + (p * -1p3 + q * -1p3 + -1r * -1p3) + -1qr * (p + q + -1r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0

Reorder the terms:
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + -1p2q2r + p2q3 + p3q2 + p2qr + -1p2r2 + p3r + (-1p3q + 1p3r + -1p4) + -1qr * (p + q + -1r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + -1p2q2r + p2q3 + p3q2 + p2qr + -1p2r2 + p3r + (-1p3q + 1p3r + -1p4) + -1qr * (p + q + -1r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + -1p2q2r + p2q3 + p3q2 + p2qr + -1p2r2 + p3r + -1p3q + 1p3r + -1p4 + (p * -1qr + q * -1qr + -1r * -1qr) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0

Reorder the terms:
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + -1p2q2r + p2q3 + p3q2 + p2qr + -1p2r2 + p3r + -1p3q + 1p3r + -1p4 + (-1pqr + 1qr2 + -1q2r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + -1p2q2r + p2q3 + p3q2 + p2qr + -1p2r2 + p3r + -1p3q + 1p3r + -1p4 + (-1pqr + 1qr2 + -1q2r) + q2r(p + q + -1r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + -1p2q2r + p2q3 + p3q2 + p2qr + -1p2r2 + p3r + -1p3q + 1p3r + -1p4 + -1pqr + 1qr2 + -1q2r + (p * q2r + q * q2r + -1r * q2r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0

Reorder the terms:
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + -1p2q2r + p2q3 + p3q2 + p2qr + -1p2r2 + p3r + -1p3q + 1p3r + -1p4 + -1pqr + 1qr2 + -1q2r + (pq2r + -1q2r2 + q3r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + -1p2q2r + p2q3 + p3q2 + p2qr + -1p2r2 + p3r + -1p3q + 1p3r + -1p4 + -1pqr + 1qr2 + -1q2r + (pq2r + -1q2r2 + q3r) + -1q3 * (p + q + -1r) + r2(p + q + -1r)) = 0
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + -1p2q2r + p2q3 + p3q2 + p2qr + -1p2r2 + p3r + -1p3q + 1p3r + -1p4 + -1pqr + 1qr2 + -1q2r + pq2r + -1q2r2 + q3r + (p * -1q3 + q * -1q3 + -1r * -1q3) + r2(p + q + -1r)) = 0

Reorder the terms:
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + -1p2q2r + p2q3 + p3q2 + p2qr + -1p2r2 + p3r + -1p3q + 1p3r + -1p4 + -1pqr + 1qr2 + -1q2r + pq2r + -1q2r2 + q3r + (-1pq3 + 1q3r + -1q4) + r2(p + q + -1r)) = 0
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + -1p2q2r + p2q3 + p3q2 + p2qr + -1p2r2 + p3r + -1p3q + 1p3r + -1p4 + -1pqr + 1qr2 + -1q2r + pq2r + -1q2r2 + q3r + (-1pq3 + 1q3r + -1q4) + r2(p + q + -1r)) = 0
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + -1p2q2r + p2q3 + p3q2 + p2qr + -1p2r2 + p3r + -1p3q + 1p3r + -1p4 + -1pqr + 1qr2 + -1q2r + pq2r + -1q2r2 + q3r + -1pq3 + 1q3r + -1q4 + (p * r2 + q * r2 + -1r * r2)) = 0
(-1pqr + 1pq2 + 1p2q + -1pqr + 1pr2 + -1p2r + -1p2q2r + p2q3 + p3q2 + p2qr + -1p2r2 + p3r + -1p3q + 1p3r + -1p4 + -1pqr + 1qr2 + -1q2r + pq2r + -1q2r2 + q3r + -1pq3 + 1q3r + -1q4 + (pr2 + qr2 + -1r3)) = 0

Reorder the terms:
(-1pqr + -1pqr + -1pqr + 1pq2 + pq2r + -1pq3 + 1pr2 + pr2 + 1p2q + p2qr + -1p2q2r + p2q3 + -1p2r + -1p2r2 + -1p3q + p3q2 + p3r + 1p3r + -1p4 + 1qr2 + qr2 + -1q2r + -1q2r2 + q3r + 1q3r + -1q4 + -1r3) = 0

Combine like terms: -1pqr + -1pqr = -2pqr
(-2pqr + -1pqr + 1pq2 + pq2r + -1pq3 + 1pr2 + pr2 + 1p2q + p2qr + -1p2q2r + p2q3 + -1p2r + -1p2r2 + -1p3q + p3q2 + p3r + 1p3r + -1p4 + 1qr2 + qr2 + -1q2r + -1q2r2 + q3r + 1q3r + -1q4 + -1r3) = 0

Combine like terms: -2pqr + -1pqr = -3pqr
(-3pqr + 1pq2 + pq2r + -1pq3 + 1pr2 + pr2 + 1p2q + p2qr + -1p2q2r + p2q3 + -1p2r + -1p2r2 + -1p3q + p3q2 + p3r + 1p3r + -1p4 + 1qr2 + qr2 + -1q2r + -1q2r2 + q3r + 1q3r + -1q4 + -1r3) = 0

Combine like terms: 1pr2 + pr2 = 2pr2
(-3pqr + 1pq2 + pq2r + -1pq3 + 2pr2 + 1p2q + p2qr + -1p2q2r + p2q3 + -1p2r + -1p2r2 + -1p3q + p3q2 + p3r + 1p3r + -1p4 + 1qr2 + qr2 + -1q2r + -1q2r2 + q3r + 1q3r + -1q4 + -1r3) = 0

Combine like terms: p3r + 1p3r = 2p3r
(-3pqr + 1pq2 + pq2r + -1pq3 + 2pr2 + 1p2q + p2qr + -1p2q2r + p2q3 + -1p2r + -1p2r2 + -1p3q + p3q2 + 2p3r + -1p4 + 1qr2 + qr2 + -1q2r + -1q2r2 + q3r + 1q3r + -1q4 + -1r3) = 0

Combine like terms: 1qr2 + qr2 = 2qr2
(-3pqr + 1pq2 + pq2r + -1pq3 + 2pr2 + 1p2q + p2qr + -1p2q2r + p2q3 + -1p2r + -1p2r2 + -1p3q + p3q2 + 2p3r + -1p4 + 2qr2 + -1q2r + -1q2r2 + q3r + 1q3r + -1q4 + -1r3) = 0

Combine like terms: q3r + 1q3r = 2q3r
(-3pqr + 1pq2 + pq2r + -1pq3 + 2pr2 + 1p2q + p2qr + -1p2q2r + p2q3 + -1p2r + -1p2r2 + -1p3q + p3q2 + 2p3r + -1p4 + 2qr2 + -1q2r + -1q2r2 + 2q3r + -1q4 + -1r3) = 0

Solving
-3pqr + 1pq2 + pq2r + -1pq3 + 2pr2 + 1p2q + p2qr + -1p2q2r + p2q3 + -1p2r + -1p2r2 + -1p3q + p3q2 + 2p3r + -1p4 + 2qr2 + -1q2r + -1q2r2 + 2q3r + -1q4 + -1r3 = 0

Solving for variable 'p'.

The solution to this equation could not be determined.

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