s^2-4sf-45f^2=

Solution for s^2-4sf-45f^2= equation:

Simplifying
s2 + -4sf + -45f2 = 0

Reorder the terms:
-4fs + -45f2 + s2 = 0

Solving
-4fs + -45f2 + s2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-5f + -1s)(9f + -1s) = 0

Subproblem 1
Set the factor '(-5f + -1s)' equal to zero and attempt to solve:

Simplifying
-5f + -1s = 0

Solving
-5f + -1s = 0

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

Add 's' to each side of the equation.
-5f + -1s + s = 0 + s

Combine like terms: -1s + s = 0
-5f + 0 = 0 + s
-5f = 0 + s
Remove the zero:
-5f = s

Divide each side by '-5'.
f = -0.2s

Simplifying
f = -0.2s
Subproblem 2
Set the factor '(9f + -1s)' equal to zero and attempt to solve:

Simplifying
9f + -1s = 0

Solving
9f + -1s = 0

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

Add 's' to each side of the equation.
9f + -1s + s = 0 + s

Combine like terms: -1s + s = 0
9f + 0 = 0 + s
9f = 0 + s
Remove the zero:
9f = s

Divide each side by '9'.
f = 0.1111111111s

Simplifying
f = 0.1111111111s
Solution
f = {-0.2s, 0.1111111111s}