f*(2-f)=1

Solution for f*(2-f)=1 equation:

Simplifying
f(2 + -1f) = 1
(2 * f + -1f * f) = 1
(2f + -1f2) = 1

Solving
2f + -1f2 = 1

Solving for variable 'f'.

Reorder the terms:
-1 + 2f + -1f2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 2f + -1f2 = 0

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

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

Simplifying
-1 + f = 0

Solving
-1 + f = 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 + f = 0 + 1

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

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

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

Simplifying
1 + -1f = 0

Solving
1 + -1f = 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 + -1f = 0 + -1

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

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

Divide each side by '-1'.
f = 1

Simplifying
f = 1
Solution
f = {1, 1}