((16n^2-8n-3))=0

Solution for ((16n^2-8n-3))=0 equation:

Simplifying
(16n2 + -8n + -3) = 0

Reorder the terms:
(-3 + -8n + 16n2) = 0

Remove parenthesis around (-3 + -8n + 16n2)
-3 + -8n + 16n2 = 0

Solving
-3 + -8n + 16n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -4n)(3 + -4n) = 0

Subproblem 1
Set the factor '(-1 + -4n)' equal to zero and attempt to solve:

Simplifying
-1 + -4n = 0

Solving
-1 + -4n = 0

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

Add '1' to each side of the equation.
-1 + 1 + -4n = 0 + 1

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

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

Divide each side by '-4'.
n = -0.25

Simplifying
n = -0.25
Subproblem 2
Set the factor '(3 + -4n)' equal to zero and attempt to solve:

Simplifying
3 + -4n = 0

Solving
3 + -4n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4n = 0 + -3
-4n = 0 + -3

Combine like terms: 0 + -3 = -3
-4n = -3

Divide each side by '-4'.
n = 0.75

Simplifying
n = 0.75
Solution
n = {-0.25, 0.75}