Solve for f g^2=mf-Rf

$g^{2} = m f - R f$

Rewrite the equation as $m f - R f = g^{2}$ .

$m f - R f = g^{2}$

Factor $f$ out of $m f - R f$ .

Factor $f$ out of $m f$ .

$f m - R f = g^{2}$

Factor $f$ out of $- R f$ .

$f m + f (- R) = g^{2}$

Factor $f$ out of $f m + f (- R)$ .

$f (m - R) = g^{2}$

Divide each term in $f (m - R) = g^{2}$ by $m - R$ and simplify.

Divide each term in $f (m - R) = g^{2}$ by $m - R$ .

$\frac{f (m - R)}{m - R} = \frac{g^{2}}{m - R}$

Simplify the left side.

Cancel the common factor of $m - R$ .

Cancel the common factor.

$\frac{f (m - R)}{m - R} = \frac{g^{2}}{m - R}$

Divide $f$ by $1$ .

$f = \frac{g^{2}}{m - R}$