(2x+1)(2x+1)=1

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

Simplifying
(2x + 1)(2x + 1) = 1

Reorder the terms:
(1 + 2x)(2x + 1) = 1

Reorder the terms:
(1 + 2x)(1 + 2x) = 1

Multiply (1 + 2x) * (1 + 2x)
(1(1 + 2x) + 2x * (1 + 2x)) = 1
((1 * 1 + 2x * 1) + 2x * (1 + 2x)) = 1
((1 + 2x) + 2x * (1 + 2x)) = 1
(1 + 2x + (1 * 2x + 2x * 2x)) = 1
(1 + 2x + (2x + 4x2)) = 1

Combine like terms: 2x + 2x = 4x
(1 + 4x + 4x2) = 1

Add '-1' to each side of the equation.
1 + 4x + -1 + 4x2 = 1 + -1

Reorder the terms:
1 + -1 + 4x + 4x2 = 1 + -1

Combine like terms: 1 + -1 = 0
0 + 4x + 4x2 = 1 + -1
4x + 4x2 = 1 + -1

Combine like terms: 1 + -1 = 0
4x + 4x2 = 0

Solving
4x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(1 + x) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {0, -1}