(a-b)(b-a)=

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

Simplifying
(a + -1b)(b + -1a) = 0

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

Multiply (a + -1b) * (-1a + b)
(a(-1a + b) + -1b * (-1a + b)) = 0
((-1a * a + b * a) + -1b * (-1a + b)) = 0

Reorder the terms:
((ab + -1a2) + -1b * (-1a + b)) = 0
((ab + -1a2) + -1b * (-1a + b)) = 0
(ab + -1a2 + (-1a * -1b + b * -1b)) = 0
(ab + -1a2 + (1ab + -1b2)) = 0

Reorder the terms:
(ab + 1ab + -1a2 + -1b2) = 0

Combine like terms: ab + 1ab = 2ab
(2ab + -1a2 + -1b2) = 0

Solving
2ab + -1a2 + -1b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1a + b)(a + -1b) = 0

Subproblem 1
Set the factor '(-1a + b)' equal to zero and attempt to solve:

Simplifying
-1a + b = 0

Solving
-1a + b = 0

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

Add '-1b' to each side of the equation.
-1a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
-1a + 0 = 0 + -1b
-1a = 0 + -1b
Remove the zero:
-1a = -1b

Divide each side by '-1'.
a = b

Simplifying
a = b
Subproblem 2
Set the factor '(a + -1b)' equal to zero and attempt to solve:

Simplifying
a + -1b = 0

Solving
a + -1b = 0

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

Add 'b' to each side of the equation.
a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
a + 0 = 0 + b
a = 0 + b
Remove the zero:
a = b

Simplifying
a = b
Solution
a = {b, b}