xyz+xyt+yzt+xzt=xyzt(x+y+z+t)

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Solution for xyz+xyt+yzt+xzt=xyzt(x+y+z+t) equation: 


Simplifying
xyz + xyt + yzt + xzt = xyzt(x + y + z + t)

Reorder the terms:
txy + txz + tyz + xyz = xyzt(x + y + z + t)

Reorder the terms:
txy + txz + tyz + xyz = txyz(t + x + y + z)
txy + txz + tyz + xyz = (t * txyz + x * txyz + y * txyz + z * txyz)

Reorder the terms:
txy + txz + tyz + xyz = (txyz2 + txy2z + tx2yz + t2xyz)
txy + txz + tyz + xyz = (txyz2 + txy2z + tx2yz + t2xyz)

Solving
txy + txz + tyz + xyz = txyz2 + txy2z + tx2yz + t2xyz

Solving for variable 't'.

Reorder the terms:
txy + -1txyz2 + -1txy2z + txz + -1tx2yz + tyz + -1t2xyz + xyz = txyz2 + txy2z + tx2yz + t2xyz + -1txyz2 + -1txy2z + -1tx2yz + -1t2xyz

Reorder the terms:
txy + -1txyz2 + -1txy2z + txz + -1tx2yz + tyz + -1t2xyz + xyz = txyz2 + -1txyz2 + txy2z + -1txy2z + tx2yz + -1tx2yz + t2xyz + -1t2xyz

Combine like terms: txyz2 + -1txyz2 = 0
txy + -1txyz2 + -1txy2z + txz + -1tx2yz + tyz + -1t2xyz + xyz = 0 + txy2z + -1txy2z + tx2yz + -1tx2yz + t2xyz + -1t2xyz
txy + -1txyz2 + -1txy2z + txz + -1tx2yz + tyz + -1t2xyz + xyz = txy2z + -1txy2z + tx2yz + -1tx2yz + t2xyz + -1t2xyz

Combine like terms: txy2z + -1txy2z = 0
txy + -1txyz2 + -1txy2z + txz + -1tx2yz + tyz + -1t2xyz + xyz = 0 + tx2yz + -1tx2yz + t2xyz + -1t2xyz
txy + -1txyz2 + -1txy2z + txz + -1tx2yz + tyz + -1t2xyz + xyz = tx2yz + -1tx2yz + t2xyz + -1t2xyz

Combine like terms: tx2yz + -1tx2yz = 0
txy + -1txyz2 + -1txy2z + txz + -1tx2yz + tyz + -1t2xyz + xyz = 0 + t2xyz + -1t2xyz
txy + -1txyz2 + -1txy2z + txz + -1tx2yz + tyz + -1t2xyz + xyz = t2xyz + -1t2xyz

Combine like terms: t2xyz + -1t2xyz = 0
txy + -1txyz2 + -1txy2z + txz + -1tx2yz + tyz + -1t2xyz + xyz = 0

The solution to this equation could not be determined.

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