(2n+1)(2n+1)=

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

Simplifying
(2n + 1)(2n + 1) = 0

Reorder the terms:
(1 + 2n)(2n + 1) = 0

Reorder the terms:
(1 + 2n)(1 + 2n) = 0

Multiply (1 + 2n) * (1 + 2n)
(1(1 + 2n) + 2n * (1 + 2n)) = 0
((1 * 1 + 2n * 1) + 2n * (1 + 2n)) = 0
((1 + 2n) + 2n * (1 + 2n)) = 0
(1 + 2n + (1 * 2n + 2n * 2n)) = 0
(1 + 2n + (2n + 4n2)) = 0

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

Solving
1 + 4n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + 2n)(1 + 2n) = 0

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

Simplifying
1 + 2n = 0

Solving
1 + 2n = 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 + 2n = 0 + -1

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

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

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

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

Simplifying
1 + 2n = 0

Solving
1 + 2n = 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 + 2n = 0 + -1

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

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

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

Simplifying
n = -0.5
Solution
n = {-0.5, -0.5}