r^2-rf-20f^2=

Solution for r^2-rf-20f^2= equation:

Simplifying
r2 + -1rf + -20f2 = 0

Reorder the terms:
-1fr + -20f2 + r2 = 0

Solving
-1fr + -20f2 + r2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-4f + -1r)(5f + -1r) = 0

Subproblem 1
Set the factor '(-4f + -1r)' equal to zero and attempt to solve:

Simplifying
-4f + -1r = 0

Solving
-4f + -1r = 0

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

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

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

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

Simplifying
f = -0.25r
Subproblem 2
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
Solution
f = {-0.25r, 0.2r}