y^2+2xy+1=x^2+2xy+1

Solution for y^2+2xy+1=x^2+2xy+1 equation:

Simplifying
y2 + 2xy + 1 = x2 + 2xy + 1

Reorder the terms:
1 + 2xy + y2 = x2 + 2xy + 1

Reorder the terms:
1 + 2xy + y2 = 1 + 2xy + x2

Add '-1' to each side of the equation.
1 + 2xy + -1 + y2 = 1 + 2xy + -1 + x2

Reorder the terms:
1 + -1 + 2xy + y2 = 1 + 2xy + -1 + x2

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

Reorder the terms:
2xy + y2 = 1 + -1 + 2xy + x2

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

Add '-2xy' to each side of the equation.
2xy + -2xy + y2 = 2xy + -2xy + x2

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

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

Solving
y2 = x2

Solving for variable 'y'.

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

Simplifying
y2 = x2

Take the square root of each side:
y = {-1x, x}