Let's start by simplifying the left side of the equation:

(1-4x)(1+4x)/4 = (1 - 16x^2)/4 = 1/4 - 4x^2

Now, let's simplify the right side of the equation:

1 - (2x - 1)(2x+1) = 1 - (4x^2 - 1) = 1 - 4x^2 + 1 = 2 - 4x^2

Now, we can set the two sides equal to each other:

1/4 - 4x^2 = 2 - 4x^2

Since both sides have -4x^2, we can subtract this term from both sides to simplify:

1/4 = 2

This is clearly not true, so there seems to be an error in the initial equation provided.