n(3n+2)=1

Solution for n(3n+2)=1 equation:

Simplifying
n(3n + 2) = 1

Reorder the terms:
n(2 + 3n) = 1
(2 * n + 3n * n) = 1
(2n + 3n2) = 1

Solving
2n + 3n2 = 1

Solving for variable 'n'.

Reorder the terms:
-1 + 2n + 3n2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 2n + 3n2 = 0

Factor a trinomial.
(-1 + -1n)(1 + -3n) = 0

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

Simplifying
-1 + -1n = 0

Solving
-1 + -1n = 0

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

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

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

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

Divide each side by '-1'.
n = -1

Simplifying
n = -1
Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve:

Simplifying
1 + -3n = 0

Solving
1 + -3n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3n = 0 + -1
-3n = 0 + -1

Combine like terms: 0 + -1 = -1
-3n = -1

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
Solution
n = {-1, 0.3333333333}