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

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

Simplifying
a(x + -1y) * b(y + -1x) = 0

Reorder the terms:
a(x + -1y) * b(-1x + y) = 0

Reorder the terms for easier multiplication:
a * b(x + -1y)(-1x + y) = 0

Multiply a * b
ab(x + -1y)(-1x + y) = 0

Multiply (x + -1y) * (-1x + y)
ab(x(-1x + y) + -1y * (-1x + y)) = 0
ab((-1x * x + y * x) + -1y * (-1x + y)) = 0

Reorder the terms:
ab((xy + -1x2) + -1y * (-1x + y)) = 0
ab((xy + -1x2) + -1y * (-1x + y)) = 0
ab(xy + -1x2 + (-1x * -1y + y * -1y)) = 0
ab(xy + -1x2 + (1xy + -1y2)) = 0

Reorder the terms:
ab(xy + 1xy + -1x2 + -1y2) = 0

Combine like terms: xy + 1xy = 2xy
ab(2xy + -1x2 + -1y2) = 0
(2xy * ab + -1x2 * ab + -1y2 * ab) = 0
(2abxy + -1abx2 + -1aby2) = 0

Solving
2abxy + -1abx2 + -1aby2 = 0

Solving for variable 'a'.

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

Factor out the Greatest Common Factor (GCF), 'ab'.
ab(2xy + -1x2 + -1y2) = 0

Factor a trinomial.
ab((-1x + y)(x + -1y)) = 0

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

Simplifying
ab = 0

Solving
ab = 0

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

Simplifying
ab = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-1x + y)' equal to zero and attempt to solve:

Simplifying
-1x + y = 0

Solving
-1x + y = 0

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

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

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

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

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

Simplifying
0 = x + -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(x + -1y)' equal to zero and attempt to solve:

Simplifying
x + -1y = 0

Solving
x + -1y = 0

Move all terms containing a 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.

The solution to this equation could not be determined.