4n^2-4n-1=-2

Solution for 4n^2-4n-1=-2 equation:

Simplifying
4n2 + -4n + -1 = -2

Reorder the terms:
-1 + -4n + 4n2 = -2

Solving
-1 + -4n + 4n2 = -2

Solving for variable 'n'.

Reorder the terms:
-1 + 2 + -4n + 4n2 = -2 + 2

Combine like terms: -1 + 2 = 1
1 + -4n + 4n2 = -2 + 2

Combine like terms: -2 + 2 = 0
1 + -4n + 4n2 = 0

Factor a trinomial.
(1 + -2n)(1 + -2n) = 0

Subproblem 1
Set the factor '(1 + -2n)' equal to zero and attempt to solve:

Simplifying
1 + -2n = 0

Solving
1 + -2n = 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 + -2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2n = 0 + -1
-2n = 0 + -1

Combine like terms: 0 + -1 = -1
-2n = -1

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
Subproblem 2
Set the factor '(1 + -2n)' equal to zero and attempt to solve:

Simplifying
1 + -2n = 0

Solving
1 + -2n = 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 + -2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2n = 0 + -1
-2n = 0 + -1

Combine like terms: 0 + -1 = -1
-2n = -1

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
Solution
n = {0.5, 0.5}