f^2-22f=23

Solution for f^2-22f=23 equation:

Simplifying
f2 + -22f = 23

Reorder the terms:
-22f + f2 = 23

Solving
-22f + f2 = 23

Solving for variable 'f'.

Reorder the terms:
-23 + -22f + f2 = 23 + -23

Combine like terms: 23 + -23 = 0
-23 + -22f + f2 = 0

Factor a trinomial.
(-1 + -1f)(23 + -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 '(23 + -1f)' equal to zero and attempt to solve:

Simplifying
23 + -1f = 0

Solving
23 + -1f = 0

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

Add '-23' to each side of the equation.
23 + -23 + -1f = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -1f = 0 + -23
-1f = 0 + -23

Combine like terms: 0 + -23 = -23
-1f = -23

Divide each side by '-1'.
f = 23

Simplifying
f = 23
Solution
f = {-1, 23}