(x^2-yz)p+(y^2-zx)q=z^2-xy

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Solution for (x^2-yz)p+(y^2-zx)q=z^2-xy equation: 


Simplifying
(x2 + -1yz) * p + (y2 + -1zx) * q = z2 + -1xy

Reorder the terms for easier multiplication:
p(x2 + -1yz) + (y2 + -1zx) * q = z2 + -1xy
(x2 * p + -1yz * p) + (y2 + -1zx) * q = z2 + -1xy
(px2 + -1pyz) + (y2 + -1zx) * q = z2 + -1xy

Reorder the terms:
px2 + -1pyz + (-1xz + y2) * q = z2 + -1xy

Reorder the terms for easier multiplication:
px2 + -1pyz + q(-1xz + y2) = z2 + -1xy
px2 + -1pyz + (-1xz * q + y2 * q) = z2 + -1xy
px2 + -1pyz + (-1qxz + qy2) = z2 + -1xy

Reorder the terms:
px2 + -1pyz + -1qxz + qy2 = -1xy + z2

Solving
px2 + -1pyz + -1qxz + qy2 = -1xy + z2

Solving for variable 'p'.

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

Add 'qxz' to each side of the equation.
px2 + -1pyz + -1qxz + qxz + qy2 = -1xy + qxz + z2

Combine like terms: -1qxz + qxz = 0
px2 + -1pyz + 0 + qy2 = -1xy + qxz + z2
px2 + -1pyz + qy2 = -1xy + qxz + z2

Reorder the terms:
px2 + -1pyz + qy2 = qxz + -1xy + z2

Add '-1qy2' to each side of the equation.
px2 + -1pyz + qy2 + -1qy2 = qxz + -1xy + -1qy2 + z2

Combine like terms: qy2 + -1qy2 = 0
px2 + -1pyz + 0 = qxz + -1xy + -1qy2 + z2
px2 + -1pyz = qxz + -1xy + -1qy2 + z2

Reorder the terms:
px2 + -1pyz = qxz + -1qy2 + -1xy + z2

Reorder the terms:
px2 + -1pyz + -1qxz + qy2 + xy + -1z2 = qxz + -1qxz + -1qy2 + qy2 + -1xy + xy + z2 + -1z2

Combine like terms: qxz + -1qxz = 0
px2 + -1pyz + -1qxz + qy2 + xy + -1z2 = 0 + -1qy2 + qy2 + -1xy + xy + z2 + -1z2
px2 + -1pyz + -1qxz + qy2 + xy + -1z2 = -1qy2 + qy2 + -1xy + xy + z2 + -1z2

Combine like terms: -1qy2 + qy2 = 0
px2 + -1pyz + -1qxz + qy2 + xy + -1z2 = 0 + -1xy + xy + z2 + -1z2
px2 + -1pyz + -1qxz + qy2 + xy + -1z2 = -1xy + xy + z2 + -1z2

Combine like terms: -1xy + xy = 0
px2 + -1pyz + -1qxz + qy2 + xy + -1z2 = 0 + z2 + -1z2
px2 + -1pyz + -1qxz + qy2 + xy + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
px2 + -1pyz + -1qxz + qy2 + xy + -1z2 = 0

The solution to this equation could not be determined.

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