lny(3-lny)=2

Solution for lny(3-lny)=2 equation:

Simplifying
lny(3 + -1lny) = 2
(3 * lny + -1lny * lny) = 2
(3lny + -1l2n2y2) = 2

Solving
3lny + -1l2n2y2 = 2

Solving for variable 'l'.

Reorder the terms:
-2 + 3lny + -1l2n2y2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 3lny + -1l2n2y2 = 0

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

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

Simplifying
-2 + lny = 0

Solving
-2 + lny = 0

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

Add '2' to each side of the equation.
-2 + 2 + lny = 0 + 2

Combine like terms: -2 + 2 = 0
0 + lny = 0 + 2
lny = 0 + 2

Combine like terms: 0 + 2 = 2
lny = 2

Divide each side by 'ny'.
l = 2n-1y-1

Simplifying
l = 2n-1y-1
Subproblem 2
Set the factor '(1 + -1lny)' equal to zero and attempt to solve:

Simplifying
1 + -1lny = 0

Solving
1 + -1lny = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1lny = 0 + -1
-1lny = 0 + -1

Combine like terms: 0 + -1 = -1
-1lny = -1

Divide each side by '-1ny'.
l = n-1y-1

Simplifying
l = n-1y-1
Solution
l = {2n-1y-1, n-1y-1}