0=12m^2n^2-8mn+1

Solution for 0=12m^2n^2-8mn+1 equation:

Simplifying
0 = 12m2n2 + -8mn + 1

Reorder the terms:
0 = 1 + -8mn + 12m2n2

Solving
0 = 1 + -8mn + 12m2n2

Solving for variable 'm'.

Combine like terms: 0 + -1 = -1
-1 + 8mn + -12m2n2 = 1 + -8mn + 12m2n2 + -1 + 8mn + -12m2n2

Reorder the terms:
-1 + 8mn + -12m2n2 = 1 + -1 + -8mn + 8mn + 12m2n2 + -12m2n2

Combine like terms: 1 + -1 = 0
-1 + 8mn + -12m2n2 = 0 + -8mn + 8mn + 12m2n2 + -12m2n2
-1 + 8mn + -12m2n2 = -8mn + 8mn + 12m2n2 + -12m2n2

Combine like terms: -8mn + 8mn = 0
-1 + 8mn + -12m2n2 = 0 + 12m2n2 + -12m2n2
-1 + 8mn + -12m2n2 = 12m2n2 + -12m2n2

Combine like terms: 12m2n2 + -12m2n2 = 0
-1 + 8mn + -12m2n2 = 0

Factor a trinomial.
(-1 + 2mn)(1 + -6mn) = 0

Subproblem 1
Set the factor '(-1 + 2mn)' equal to zero and attempt to solve:

Simplifying
-1 + 2mn = 0

Solving
-1 + 2mn = 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 + 2mn = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2mn = 0 + 1
2mn = 0 + 1

Combine like terms: 0 + 1 = 1
2mn = 1

Divide each side by '2n'.
m = 0.5n-1

Simplifying
m = 0.5n-1
Subproblem 2
Set the factor '(1 + -6mn)' equal to zero and attempt to solve:

Simplifying
1 + -6mn = 0

Solving
1 + -6mn = 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 + -6mn = 0 + -1

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

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

Divide each side by '-6n'.
m = 0.1666666667n-1

Simplifying
m = 0.1666666667n-1
Solution
m = {0.5n-1, 0.1666666667n-1}