f^2-18f+72=0

Solution for f^2-18f+72=0 equation:

Simplifying
f2 + -18f + 72 = 0

Reorder the terms:
72 + -18f + f2 = 0

Solving
72 + -18f + f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(6 + -1f)(12 + -1f) = 0

Subproblem 1
Set the factor '(6 + -1f)' equal to zero and attempt to solve:

Simplifying
6 + -1f = 0

Solving
6 + -1f = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1f = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1f = 0 + -6
-1f = 0 + -6

Combine like terms: 0 + -6 = -6
-1f = -6

Divide each side by '-1'.
f = 6

Simplifying
f = 6
Subproblem 2
Set the factor '(12 + -1f)' equal to zero and attempt to solve:

Simplifying
12 + -1f = 0

Solving
12 + -1f = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1f = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1f = 0 + -12
-1f = 0 + -12

Combine like terms: 0 + -12 = -12
-1f = -12

Divide each side by '-1'.
f = 12

Simplifying
f = 12
Solution
f = {6, 12}