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

Solution for (4n+1)(4n-1)=0 equation:

Simplifying
(4n + 1)(4n + -1) = 0

Reorder the terms:
(1 + 4n)(4n + -1) = 0

Reorder the terms:
(1 + 4n)(-1 + 4n) = 0

Multiply (1 + 4n) * (-1 + 4n)
(1(-1 + 4n) + 4n * (-1 + 4n)) = 0
((-1 * 1 + 4n * 1) + 4n * (-1 + 4n)) = 0
((-1 + 4n) + 4n * (-1 + 4n)) = 0
(-1 + 4n + (-1 * 4n + 4n * 4n)) = 0
(-1 + 4n + (-4n + 16n2)) = 0

Combine like terms: 4n + -4n = 0
(-1 + 0 + 16n2) = 0
(-1 + 16n2) = 0

Solving
-1 + 16n2 = 0

Solving for variable 'n'.

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

Add '1' to each side of the equation.
-1 + 1 + 16n2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 16n2 = 0 + 1
16n2 = 0 + 1

Combine like terms: 0 + 1 = 1
16n2 = 1

Divide each side by '16'.
n2 = 0.0625

Simplifying
n2 = 0.0625

Take the square root of each side:
n = {-0.25, 0.25}