-4f^2+4f-1=0

Solution for -4f^2+4f-1=0 equation:

Simplifying
-4f2 + 4f + -1 = 0

Reorder the terms:
-1 + 4f + -4f2 = 0

Solving
-1 + 4f + -4f2 = 0

Solving for variable 'f'.

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

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

Simplifying
-1 + 2f = 0

Solving
-1 + 2f = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2f = 0 + 1

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

Combine like terms: 0 + 1 = 1
2f = 1

Divide each side by '2'.
f = 0.5

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

Simplifying
1 + -2f = 0

Solving
1 + -2f = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2f = 0 + -1

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

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

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

Simplifying
f = 0.5
Solution
f = {0.5, 0.5}