px(y^2+z)-qy(x^2+z)=z(x^2-y^2)

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Solution for px(y^2+z)-qy(x^2+z)=z(x^2-y^2) equation: 


Simplifying
px(y2 + z) + -1qy(x2 + z) = z(x2 + -1y2)
(y2 * px + z * px) + -1qy(x2 + z) = z(x2 + -1y2)
(pxy2 + pxz) + -1qy(x2 + z) = z(x2 + -1y2)
pxy2 + pxz + (x2 * -1qy + z * -1qy) = z(x2 + -1y2)
pxy2 + pxz + (-1qx2y + -1qyz) = z(x2 + -1y2)
pxy2 + pxz + -1qx2y + -1qyz = (x2 * z + -1y2 * z)
pxy2 + pxz + -1qx2y + -1qyz = (x2z + -1y2z)

Solving
pxy2 + pxz + -1qx2y + -1qyz = x2z + -1y2z

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add 'qx2y' to each side of the equation.
pxy2 + pxz + -1qx2y + qx2y + -1qyz = x2z + qx2y + -1y2z

Combine like terms: -1qx2y + qx2y = 0
pxy2 + pxz + 0 + -1qyz = x2z + qx2y + -1y2z
pxy2 + pxz + -1qyz = x2z + qx2y + -1y2z

Reorder the terms:
pxy2 + pxz + -1qyz = qx2y + x2z + -1y2z

Add 'qyz' to each side of the equation.
pxy2 + pxz + -1qyz + qyz = qx2y + x2z + qyz + -1y2z

Combine like terms: -1qyz + qyz = 0
pxy2 + pxz + 0 = qx2y + x2z + qyz + -1y2z
pxy2 + pxz = qx2y + x2z + qyz + -1y2z

Reorder the terms:
pxy2 + pxz = qx2y + qyz + x2z + -1y2z

Reorder the terms:
pxy2 + pxz + -1qx2y + -1qyz + -1x2z + y2z = qx2y + -1qx2y + qyz + -1qyz + x2z + -1x2z + -1y2z + y2z

Combine like terms: qx2y + -1qx2y = 0
pxy2 + pxz + -1qx2y + -1qyz + -1x2z + y2z = 0 + qyz + -1qyz + x2z + -1x2z + -1y2z + y2z
pxy2 + pxz + -1qx2y + -1qyz + -1x2z + y2z = qyz + -1qyz + x2z + -1x2z + -1y2z + y2z

Combine like terms: qyz + -1qyz = 0
pxy2 + pxz + -1qx2y + -1qyz + -1x2z + y2z = 0 + x2z + -1x2z + -1y2z + y2z
pxy2 + pxz + -1qx2y + -1qyz + -1x2z + y2z = x2z + -1x2z + -1y2z + y2z

Combine like terms: x2z + -1x2z = 0
pxy2 + pxz + -1qx2y + -1qyz + -1x2z + y2z = 0 + -1y2z + y2z
pxy2 + pxz + -1qx2y + -1qyz + -1x2z + y2z = -1y2z + y2z

Combine like terms: -1y2z + y2z = 0
pxy2 + pxz + -1qx2y + -1qyz + -1x2z + y2z = 0

The solution to this equation could not be determined.

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