(2a-1)(2a+1)=1

Solution for (2a-1)(2a+1)=1 equation:

Simplifying
(2a + -1)(2a + 1) = 1

Reorder the terms:
(-1 + 2a)(2a + 1) = 1

Reorder the terms:
(-1 + 2a)(1 + 2a) = 1

Multiply (-1 + 2a) * (1 + 2a)
(-1(1 + 2a) + 2a * (1 + 2a)) = 1
((1 * -1 + 2a * -1) + 2a * (1 + 2a)) = 1
((-1 + -2a) + 2a * (1 + 2a)) = 1
(-1 + -2a + (1 * 2a + 2a * 2a)) = 1
(-1 + -2a + (2a + 4a2)) = 1

Combine like terms: -2a + 2a = 0
(-1 + 0 + 4a2) = 1
(-1 + 4a2) = 1

Solving
-1 + 4a2 = 1

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + 4a2 = 1 + 1

Combine like terms: -1 + 1 = 0
0 + 4a2 = 1 + 1
4a2 = 1 + 1

Combine like terms: 1 + 1 = 2
4a2 = 2

Divide each side by '4'.
a2 = 0.5

Simplifying
a2 = 0.5

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