36x^2y^2+12xy+1=0

Solution for 36x^2y^2+12xy+1=0 equation:

Simplifying
36x2y2 + 12xy + 1 = 0

Reorder the terms:
1 + 12xy + 36x2y2 = 0

Solving
1 + 12xy + 36x2y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + 6xy)(1 + 6xy) = 0

Subproblem 1
Set the factor '(1 + 6xy)' equal to zero and attempt to solve:

Simplifying
1 + 6xy = 0

Solving
1 + 6xy = 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 + 6xy = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6xy = 0 + -1
6xy = 0 + -1

Combine like terms: 0 + -1 = -1
6xy = -1

Divide each side by '6y'.
x = -0.1666666667y-1

Simplifying
x = -0.1666666667y-1
Subproblem 2
Set the factor '(1 + 6xy)' equal to zero and attempt to solve:

Simplifying
1 + 6xy = 0

Solving
1 + 6xy = 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 + 6xy = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6xy = 0 + -1
6xy = 0 + -1

Combine like terms: 0 + -1 = -1
6xy = -1

Divide each side by '6y'.
x = -0.1666666667y-1

Simplifying
x = -0.1666666667y-1
Solution
x = {-0.1666666667y-1, -0.1666666667y-1}