(2k+1)(2k+1)=

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

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

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

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

Multiply (1 + 2k) * (1 + 2k)
(1(1 + 2k) + 2k * (1 + 2k)) = 0
((1 * 1 + 2k * 1) + 2k * (1 + 2k)) = 0
((1 + 2k) + 2k * (1 + 2k)) = 0
(1 + 2k + (1 * 2k + 2k * 2k)) = 0
(1 + 2k + (2k + 4k2)) = 0

Combine like terms: 2k + 2k = 4k
(1 + 4k + 4k2) = 0

Solving
1 + 4k + 4k2 = 0

Solving for variable 'k'.

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

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

Simplifying
1 + 2k = 0

Solving
1 + 2k = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2k = 0 + -1

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

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

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

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

Simplifying
1 + 2k = 0

Solving
1 + 2k = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2k = 0 + -1

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

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

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

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