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

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

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

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

Multiply x * p
px(y + z) + (z + x) * q = x + y
(y * px + z * px) + (z + x) * q = x + y
(pxy + pxz) + (z + x) * q = x + y

Reorder the terms:
pxy + pxz + (x + z) * q = x + y

Reorder the terms for easier multiplication:
pxy + pxz + q(x + z) = x + y
pxy + pxz + (x * q + z * q) = x + y
pxy + pxz + (qx + qz) = x + y

Solving
pxy + pxz + qx + qz = x + y

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.
pxy + pxz + qx + -1qx + qz = x + -1qx + y

Combine like terms: qx + -1qx = 0
pxy + pxz + 0 + qz = x + -1qx + y
pxy + pxz + qz = x + -1qx + y

Reorder the terms:
pxy + pxz + qz = -1qx + x + y

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

Combine like terms: qz + -1qz = 0
pxy + pxz + 0 = -1qx + x + -1qz + y
pxy + pxz = -1qx + x + -1qz + y

Reorder the terms:
pxy + pxz = -1qx + -1qz + x + y

Reorder the terms:
pxy + pxz + qx + qz + -1x + -1y = -1qx + qx + -1qz + qz + x + -1x + y + -1y

Combine like terms: -1qx + qx = 0
pxy + pxz + qx + qz + -1x + -1y = 0 + -1qz + qz + x + -1x + y + -1y
pxy + pxz + qx + qz + -1x + -1y = -1qz + qz + x + -1x + y + -1y

Combine like terms: -1qz + qz = 0
pxy + pxz + qx + qz + -1x + -1y = 0 + x + -1x + y + -1y
pxy + pxz + qx + qz + -1x + -1y = x + -1x + y + -1y

Combine like terms: x + -1x = 0
pxy + pxz + qx + qz + -1x + -1y = 0 + y + -1y
pxy + pxz + qx + qz + -1x + -1y = y + -1y

Combine like terms: y + -1y = 0
pxy + pxz + qx + qz + -1x + -1y = 0

The solution to this equation could not be determined.