r^2-7rf+12f^2=0

Solution for r^2-7rf+12f^2=0 equation:

Simplifying
r2 + -7rf + 12f2 = 0

Reorder the terms:
-7fr + 12f2 + r2 = 0

Solving
-7fr + 12f2 + r2 = 0

Solving for variable 'f'.

Factor a trinomial.
(3f + -1r)(4f + -1r) = 0

Subproblem 1
Set the factor '(3f + -1r)' equal to zero and attempt to solve:

Simplifying
3f + -1r = 0

Solving
3f + -1r = 0

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

Add 'r' to each side of the equation.
3f + -1r + r = 0 + r

Combine like terms: -1r + r = 0
3f + 0 = 0 + r
3f = 0 + r
Remove the zero:
3f = r

Divide each side by '3'.
f = 0.3333333333r

Simplifying
f = 0.3333333333r
Subproblem 2
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
Solution
f = {0.3333333333r, 0.25r}