r^2-4rf-45f^2=

Solution for r^2-4rf-45f^2= equation:

Simplifying
r2 + -4rf + -45f2 = 0

Reorder the terms:
-4fr + -45f2 + r2 = 0

Solving
-4fr + -45f2 + r2 = 0

Solving for variable 'f'.

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

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

Simplifying
-5f + -1r = 0

Solving
-5f + -1r = 0

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

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

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

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

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

Simplifying
9f + -1r = 0

Solving
9f + -1r = 0

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

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

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

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

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