(2n+1)=3n^2

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

Simplifying
(2n + 1) = 3n2

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

Remove parenthesis around (1 + 2n)
1 + 2n = 3n2

Solving
1 + 2n = 3n2

Solving for variable 'n'.

Combine like terms: 3n2 + -3n2 = 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}