x+y(1-q)=y+x(1-q)

Solution for x+y(1-q)=y+x(1-q) equation:

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

Reorder the terms:
x + (-1qy + 1y) = y + x(1 + -1q)
x + (-1qy + 1y) = y + x(1 + -1q)

Reorder the terms:
-1qy + x + 1y = y + x(1 + -1q)
-1qy + x + 1y = y + (1 * x + -1q * x)

Reorder the terms:
-1qy + x + 1y = y + (-1qx + 1x)
-1qy + x + 1y = y + (-1qx + 1x)

Reorder the terms:
-1qy + x + 1y = -1qx + 1x + y

Solving
-1qy + x + 1y = -1qx + 1x + y

Solving for variable 'q'.

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

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

Reorder the terms:
qx + -1qy + x + 1y = -1qx + 1x + qx + y

Reorder the terms:
qx + -1qy + x + 1y = -1qx + qx + 1x + y

Combine like terms: -1qx + qx = 0
qx + -1qy + x + 1y = 0 + 1x + y
qx + -1qy + x + 1y = 1x + y

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

Combine like terms: x + -1x = 0
qx + -1qy + 0 + 1y = 1x + -1x + y
qx + -1qy + 1y = 1x + -1x + y

Combine like terms: 1x + -1x = 0
qx + -1qy + 1y = 0 + y
qx + -1qy + 1y = y

Add '-1y' to each side of the equation.
qx + -1qy + 1y + -1y = y + -1y

Combine like terms: 1y + -1y = 0
qx + -1qy + 0 = y + -1y
qx + -1qy = y + -1y

Combine like terms: y + -1y = 0
qx + -1qy = 0

Factor out the Greatest Common Factor (GCF), 'q'.
q(x + -1y) = 0

Subproblem 1
Set the factor 'q' equal to zero and attempt to solve:

Simplifying
q = 0

Solving
q = 0

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

Simplifying
q = 0
Subproblem 2
Set the factor '(x + -1y)' equal to zero and attempt to solve:

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

Add '-1x' to each side of the equation.
x + -1x + -1y = 0 + -1x

Combine like terms: x + -1x = 0
0 + -1y = 0 + -1x
-1y = 0 + -1x
Remove the zero:
-1y = -1x

Add 'y' to each side of the equation.
-1y + y = -1x + y

Combine like terms: -1y + y = 0
0 = -1x + y

Simplifying
0 = -1x + y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
q = {0}