f^2=4f-3

Solution for f^2=4f-3 equation:

Simplifying
f2 = 4f + -3

Reorder the terms:
f2 = -3 + 4f

Solving
f2 = -3 + 4f

Solving for variable 'f'.

Reorder the terms:
3 + -4f + f2 = -3 + 4f + 3 + -4f

Reorder the terms:
3 + -4f + f2 = -3 + 3 + 4f + -4f

Combine like terms: -3 + 3 = 0
3 + -4f + f2 = 0 + 4f + -4f
3 + -4f + f2 = 4f + -4f

Combine like terms: 4f + -4f = 0
3 + -4f + f2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1f)' equal to zero and attempt to solve:

Simplifying
3 + -1f = 0

Solving
3 + -1f = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1f = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1f = 0 + -3
-1f = 0 + -3

Combine like terms: 0 + -3 = -3
-1f = -3

Divide each side by '-1'.
f = 3

Simplifying
f = 3
Solution
f = {1, 3}