f^2+22f+21=0

Solution for f^2+22f+21=0 equation:

Simplifying
f2 + 22f + 21 = 0

Reorder the terms:
21 + 22f + f2 = 0

Solving
21 + 22f + f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(21 + f)(1 + f) = 0

Subproblem 1
Set the factor '(21 + f)' equal to zero and attempt to solve:

Simplifying
21 + f = 0

Solving
21 + f = 0

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

Add '-21' to each side of the equation.
21 + -21 + f = 0 + -21

Combine like terms: 21 + -21 = 0
0 + f = 0 + -21
f = 0 + -21

Combine like terms: 0 + -21 = -21
f = -21

Simplifying
f = -21
Subproblem 2
Set the factor '(1 + f)' equal to zero and attempt to solve:

Simplifying
1 + f = 0

Solving
1 + f = 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 + f = 0 + -1

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

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

Simplifying
f = -1
Solution
f = {-21, -1}