f^2-10f+9=0

Solution for f^2-10f+9=0 equation:

Simplifying
f2 + -10f + 9 = 0

Reorder the terms:
9 + -10f + f2 = 0

Solving
9 + -10f + f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(1 + -1f)(9 + -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 '(9 + -1f)' equal to zero and attempt to solve:

Simplifying
9 + -1f = 0

Solving
9 + -1f = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1f = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1f = 0 + -9
-1f = 0 + -9

Combine like terms: 0 + -9 = -9
-1f = -9

Divide each side by '-1'.
f = 9

Simplifying
f = 9
Solution
f = {1, 9}