(3x+y-z)p+(x+y-z)q=2(z-y)

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Solution for (3x+y-z)p+(x+y-z)q=2(z-y) equation: 


Simplifying
(3x + y + -1z) * p + (x + y + -1z) * q = 2(z + -1y)

Reorder the terms for easier multiplication:
p(3x + y + -1z) + (x + y + -1z) * q = 2(z + -1y)
(3x * p + y * p + -1z * p) + (x + y + -1z) * q = 2(z + -1y)
(3px + py + -1pz) + (x + y + -1z) * q = 2(z + -1y)

Reorder the terms for easier multiplication:
3px + py + -1pz + q(x + y + -1z) = 2(z + -1y)
3px + py + -1pz + (x * q + y * q + -1z * q) = 2(z + -1y)
3px + py + -1pz + (qx + qy + -1qz) = 2(z + -1y)

Reorder the terms:
3px + py + -1pz + qx + qy + -1qz = 2(-1y + z)
3px + py + -1pz + qx + qy + -1qz = (-1y * 2 + z * 2)
3px + py + -1pz + qx + qy + -1qz = (-2y + 2z)

Solving
3px + py + -1pz + qx + qy + -1qz = -2y + 2z

Solving for variable 'p'.

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

Add '-1qx' to each side of the equation.
3px + py + -1pz + qx + qy + -1qx + -1qz = -2y + -1qx + 2z

Reorder the terms:
3px + py + -1pz + qx + -1qx + qy + -1qz = -2y + -1qx + 2z

Combine like terms: qx + -1qx = 0
3px + py + -1pz + 0 + qy + -1qz = -2y + -1qx + 2z
3px + py + -1pz + qy + -1qz = -2y + -1qx + 2z

Reorder the terms:
3px + py + -1pz + qy + -1qz = -1qx + -2y + 2z

Add '-1qy' to each side of the equation.
3px + py + -1pz + qy + -1qy + -1qz = -1qx + -2y + -1qy + 2z

Combine like terms: qy + -1qy = 0
3px + py + -1pz + 0 + -1qz = -1qx + -2y + -1qy + 2z
3px + py + -1pz + -1qz = -1qx + -2y + -1qy + 2z

Reorder the terms:
3px + py + -1pz + -1qz = -1qx + -1qy + -2y + 2z

Add 'qz' to each side of the equation.
3px + py + -1pz + -1qz + qz = -1qx + -1qy + -2y + qz + 2z

Combine like terms: -1qz + qz = 0
3px + py + -1pz + 0 = -1qx + -1qy + -2y + qz + 2z
3px + py + -1pz = -1qx + -1qy + -2y + qz + 2z

Reorder the terms:
3px + py + -1pz = -1qx + -1qy + qz + -2y + 2z

Reorder the terms:
3px + py + -1pz + qx + qy + -1qz + 2y + -2z = -1qx + qx + -1qy + qy + qz + -1qz + -2y + 2y + 2z + -2z

Combine like terms: -1qx + qx = 0
3px + py + -1pz + qx + qy + -1qz + 2y + -2z = 0 + -1qy + qy + qz + -1qz + -2y + 2y + 2z + -2z
3px + py + -1pz + qx + qy + -1qz + 2y + -2z = -1qy + qy + qz + -1qz + -2y + 2y + 2z + -2z

Combine like terms: -1qy + qy = 0
3px + py + -1pz + qx + qy + -1qz + 2y + -2z = 0 + qz + -1qz + -2y + 2y + 2z + -2z
3px + py + -1pz + qx + qy + -1qz + 2y + -2z = qz + -1qz + -2y + 2y + 2z + -2z

Combine like terms: qz + -1qz = 0
3px + py + -1pz + qx + qy + -1qz + 2y + -2z = 0 + -2y + 2y + 2z + -2z
3px + py + -1pz + qx + qy + -1qz + 2y + -2z = -2y + 2y + 2z + -2z

Combine like terms: -2y + 2y = 0
3px + py + -1pz + qx + qy + -1qz + 2y + -2z = 0 + 2z + -2z
3px + py + -1pz + qx + qy + -1qz + 2y + -2z = 2z + -2z

Combine like terms: 2z + -2z = 0
3px + py + -1pz + qx + qy + -1qz + 2y + -2z = 0

The solution to this equation could not be determined.

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