81m^2n^2+18mn+1=0

Solution for 81m^2n^2+18mn+1=0 equation:

Simplifying
81m2n2 + 18mn + 1 = 0

Reorder the terms:
1 + 18mn + 81m2n2 = 0

Solving
1 + 18mn + 81m2n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(1 + 9mn)(1 + 9mn) = 0

Subproblem 1
Set the factor '(1 + 9mn)' equal to zero and attempt to solve:

Simplifying
1 + 9mn = 0

Solving
1 + 9mn = 0

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

Add '-1' to each side of the equation.
1 + -1 + 9mn = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9mn = 0 + -1
9mn = 0 + -1

Combine like terms: 0 + -1 = -1
9mn = -1

Divide each side by '9n'.
m = -0.1111111111n-1

Simplifying
m = -0.1111111111n-1
Subproblem 2
Set the factor '(1 + 9mn)' equal to zero and attempt to solve:

Simplifying
1 + 9mn = 0

Solving
1 + 9mn = 0

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

Add '-1' to each side of the equation.
1 + -1 + 9mn = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9mn = 0 + -1
9mn = 0 + -1

Combine like terms: 0 + -1 = -1
9mn = -1

Divide each side by '9n'.
m = -0.1111111111n-1

Simplifying
m = -0.1111111111n-1
Solution
m = {-0.1111111111n-1, -0.1111111111n-1}