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.
(-7 + -1f)(3 + -1f) = 0

Subproblem 1
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
Subproblem 2
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
Solution
f = {-7, 3}