(y+z)p-(x+z)q=x-y

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Solution for (y+z)p-(x+z)q=x-y equation: 


Simplifying
(y + z) * p + -1(x + z) * q = x + -1y

Reorder the terms for easier multiplication:
p(y + z) + -1(x + z) * q = x + -1y
(y * p + z * p) + -1(x + z) * q = x + -1y
(py + pz) + -1(x + z) * q = x + -1y

Reorder the terms for easier multiplication:
py + pz + -1q(x + z) = x + -1y
py + pz + (x * -1q + z * -1q) = x + -1y
py + pz + (-1qx + -1qz) = x + -1y

Solving
py + pz + -1qx + -1qz = x + -1y

Solving for variable 'p'.

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

Add 'qx' to each side of the equation.
py + pz + -1qx + qx + -1qz = x + qx + -1y

Combine like terms: -1qx + qx = 0
py + pz + 0 + -1qz = x + qx + -1y
py + pz + -1qz = x + qx + -1y

Reorder the terms:
py + pz + -1qz = qx + x + -1y

Add 'qz' to each side of the equation.
py + pz + -1qz + qz = qx + x + qz + -1y

Combine like terms: -1qz + qz = 0
py + pz + 0 = qx + x + qz + -1y
py + pz = qx + x + qz + -1y

Reorder the terms:
py + pz = qx + qz + x + -1y

Reorder the terms:
py + pz + -1qx + -1qz + -1x + y = qx + -1qx + qz + -1qz + x + -1x + -1y + y

Combine like terms: qx + -1qx = 0
py + pz + -1qx + -1qz + -1x + y = 0 + qz + -1qz + x + -1x + -1y + y
py + pz + -1qx + -1qz + -1x + y = qz + -1qz + x + -1x + -1y + y

Combine like terms: qz + -1qz = 0
py + pz + -1qx + -1qz + -1x + y = 0 + x + -1x + -1y + y
py + pz + -1qx + -1qz + -1x + y = x + -1x + -1y + y

Combine like terms: x + -1x = 0
py + pz + -1qx + -1qz + -1x + y = 0 + -1y + y
py + pz + -1qx + -1qz + -1x + y = -1y + y

Combine like terms: -1y + y = 0
py + pz + -1qx + -1qz + -1x + y = 0

The solution to this equation could not be determined.

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