(x+-1y)(x+-1y)=0

Solution for (x+-1y)(x+-1y)=0 equation:

Simplifying
(x + -1y)(x + -1y) = 0

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

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

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

Combine like terms: -1xy + -1xy = -2xy
(-2xy + x2 + 1y2) = 0

Solving
-2xy + x2 + 1y2 = 0

Solving for variable 'x'.

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

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

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

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

Simplifying
x = y
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 x to the left, all other terms to the right.

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

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

Simplifying
x = y
Solution
x = {y, y}