f^2-10f+21=0

Solution for f^2-10f+21=0 equation:

Simplifying
f2 + -10f + 21 = 0

Reorder the terms:
21 + -10f + f2 = 0

Solving
21 + -10f + f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(3 + -1f)(7 + -1f) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -1f)' equal to zero and attempt to solve:

Simplifying
7 + -1f = 0

Solving
7 + -1f = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1f = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1f = 0 + -7
-1f = 0 + -7

Combine like terms: 0 + -7 = -7
-1f = -7

Divide each side by '-1'.
f = 7

Simplifying
f = 7
Solution
f = {3, 7}