(2n+1)=4n^2+2n

Solution for (2n+1)=4n^2+2n equation:

Simplifying
(2n + 1) = 4n2 + 2n

Reorder the terms:
(1 + 2n) = 4n2 + 2n

Remove parenthesis around (1 + 2n)
1 + 2n = 4n2 + 2n

Reorder the terms:
1 + 2n = 2n + 4n2

Add '-2n' to each side of the equation.
1 + 2n + -2n = 2n + -2n + 4n2

Combine like terms: 2n + -2n = 0
1 + 0 = 2n + -2n + 4n2
1 = 2n + -2n + 4n2

Combine like terms: 2n + -2n = 0
1 = 0 + 4n2
1 = 4n2

Solving
1 = 4n2

Solving for variable 'n'.

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

Add '-4n2' to each side of the equation.
1 + -4n2 = 4n2 + -4n2

Combine like terms: 4n2 + -4n2 = 0
1 + -4n2 = 0

Add '-1' to each side of the equation.
1 + -1 + -4n2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4n2 = 0 + -1
-4n2 = 0 + -1

Combine like terms: 0 + -1 = -1
-4n2 = -1

Divide each side by '-4'.
n2 = 0.25

Simplifying
n2 = 0.25

Take the square root of each side:
n = {-0.5, 0.5}