0=1-xy-20x^2y^2

Solution for 0=1-xy-20x^2y^2 equation:

Simplifying
0 = 1 + -1xy + -20x2y2

Solving
0 = 1 + -1xy + -20x2y2

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + xy + 20x2y2 = 1 + -1xy + -20x2y2 + -1 + xy + 20x2y2

Reorder the terms:
-1 + xy + 20x2y2 = 1 + -1 + -1xy + xy + -20x2y2 + 20x2y2

Combine like terms: 1 + -1 = 0
-1 + xy + 20x2y2 = 0 + -1xy + xy + -20x2y2 + 20x2y2
-1 + xy + 20x2y2 = -1xy + xy + -20x2y2 + 20x2y2

Combine like terms: -1xy + xy = 0
-1 + xy + 20x2y2 = 0 + -20x2y2 + 20x2y2
-1 + xy + 20x2y2 = -20x2y2 + 20x2y2

Combine like terms: -20x2y2 + 20x2y2 = 0
-1 + xy + 20x2y2 = 0

Factor a trinomial.
(-1 + -4xy)(1 + -5xy) = 0

Subproblem 1
Set the factor '(-1 + -4xy)' equal to zero and attempt to solve:

Simplifying
-1 + -4xy = 0

Solving
-1 + -4xy = 0

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

Add '1' to each side of the equation.
-1 + 1 + -4xy = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4xy = 0 + 1
-4xy = 0 + 1

Combine like terms: 0 + 1 = 1
-4xy = 1

Divide each side by '-4y'.
x = -0.25y-1

Simplifying
x = -0.25y-1
Subproblem 2
Set the factor '(1 + -5xy)' equal to zero and attempt to solve:

Simplifying
1 + -5xy = 0

Solving
1 + -5xy = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5xy = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5xy = 0 + -1
-5xy = 0 + -1

Combine like terms: 0 + -1 = -1
-5xy = -1

Divide each side by '-5y'.
x = 0.2y-1

Simplifying
x = 0.2y-1
Solution
x = {-0.25y-1, 0.2y-1}