(xy-1)(xy+1)=400

Solution for (xy-1)(xy+1)=400 equation:

Simplifying
(xy + -1)(xy + 1) = 400

Reorder the terms:
(-1 + xy)(xy + 1) = 400

Reorder the terms:
(-1 + xy)(1 + xy) = 400

Multiply (-1 + xy) * (1 + xy)
(-1(1 + xy) + xy(1 + xy)) = 400
((1 * -1 + xy * -1) + xy(1 + xy)) = 400
((-1 + -1xy) + xy(1 + xy)) = 400
(-1 + -1xy + (1 * xy + xy * xy)) = 400
(-1 + -1xy + (1xy + x2y2)) = 400

Combine like terms: -1xy + 1xy = 0
(-1 + 0 + x2y2) = 400
(-1 + x2y2) = 400

Solving
-1 + x2y2 = 400

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x2y2 = 400 + 1

Combine like terms: -1 + 1 = 0
0 + x2y2 = 400 + 1
x2y2 = 400 + 1

Combine like terms: 400 + 1 = 401
x2y2 = 401

Divide each side by 'y2'.
x2 = 401y-2

Simplifying
x2 = 401y-2

Take the square root of each side:
x = {-20.024984395y-1, 20.024984395y-1}