s^2+11sf+28f^2=0

Solution for s^2+11sf+28f^2=0 equation:

Simplifying
s2 + 11sf + 28f2 = 0

Reorder the terms:
11fs + 28f2 + s2 = 0

Solving
11fs + 28f2 + s2 = 0

Solving for variable 'f'.

Factor a trinomial.
(7f + s)(4f + s) = 0

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

Simplifying
7f + s = 0

Solving
7f + s = 0

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

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

Combine like terms: s + -1s = 0
7f + 0 = 0 + -1s
7f = 0 + -1s
Remove the zero:
7f = -1s

Divide each side by '7'.
f = -0.1428571429s

Simplifying
f = -0.1428571429s
Subproblem 2
Set the factor '(4f + s)' equal to zero and attempt to solve:

Simplifying
4f + s = 0

Solving
4f + s = 0

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

Add '-1s' to each side of the equation.
4f + s + -1s = 0 + -1s

Combine like terms: s + -1s = 0
4f + 0 = 0 + -1s
4f = 0 + -1s
Remove the zero:
4f = -1s

Divide each side by '4'.
f = -0.25s

Simplifying
f = -0.25s
Solution
f = {-0.1428571429s, -0.25s}