(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 = 0
(-1 + 0 + 4x2) = 1
(-1 + 4x2) = 1

Solving
-1 + 4x2 = 1

Solving for variable 'x'.

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

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

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

Combine like terms: 1 + 1 = 2
4x2 = 2

Divide each side by '4'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}