f^2-4f-21=0

Solution for f^2-4f-21=0 equation:

Simplifying
f2 + -4f + -21 = 0

Reorder the terms:
-21 + -4f + f2 = 0

Solving
-21 + -4f + 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}