a(x-y)=b(y-x)

Solution for a(x-y)=b(y-x) equation:

Simplifying
a(x + -1y) = b(y + -1x)
(x * a + -1y * a) = b(y + -1x)
(ax + -1ay) = b(y + -1x)

Reorder the terms:
ax + -1ay = b(-1x + y)
ax + -1ay = (-1x * b + y * b)
ax + -1ay = (-1bx + by)

Solving
ax + -1ay = -1bx + by

Solving for variable 'a'.

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

Reorder the terms:
ax + -1ay + bx + -1by = -1bx + bx + by + -1by

Combine like terms: -1bx + bx = 0
ax + -1ay + bx + -1by = 0 + by + -1by
ax + -1ay + bx + -1by = by + -1by

Combine like terms: by + -1by = 0
ax + -1ay + bx + -1by = 0

The solution to this equation could not be determined.