(2z+1)(2z+1)=0

Solution for (2z+1)(2z+1)=0 equation:

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

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

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

Multiply (1 + 2z) * (1 + 2z)
(1(1 + 2z) + 2z * (1 + 2z)) = 0
((1 * 1 + 2z * 1) + 2z * (1 + 2z)) = 0
((1 + 2z) + 2z * (1 + 2z)) = 0
(1 + 2z + (1 * 2z + 2z * 2z)) = 0
(1 + 2z + (2z + 4z2)) = 0

Combine like terms: 2z + 2z = 4z
(1 + 4z + 4z2) = 0

Solving
1 + 4z + 4z2 = 0

Solving for variable 'z'.

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

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

Simplifying
1 + 2z = 0

Solving
1 + 2z = 0

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

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

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

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

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

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

Simplifying
1 + 2z = 0

Solving
1 + 2z = 0

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

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

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

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

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

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