Solve for m f=-(gmn)/(r^2)

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

Step 1

Rewrite the equation as $- \frac{g m n}{r^{2}} = f$ .

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

Step 2

Divide each term in $- \frac{g m n}{r^{2}} = f$ by $- 1$ and simplify.

Divide each term in $- \frac{g m n}{r^{2}} = f$ by $- 1$ .

$\frac{- \frac{g m n}{r^{2}}}{- 1} = \frac{f}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{g m n}{r^{2}}}{1} = \frac{f}{- 1}$

Divide $\frac{g m n}{r^{2}}$ by $1$ .

$\frac{g m n}{r^{2}} = \frac{f}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{f}{- 1}$ .

$\frac{g m n}{r^{2}} = - 1 \cdot f$

Rewrite $- 1 \cdot f$ as $- f$ .

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

Step 3

Multiply both sides by $r^{2}$ .

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

Step 4

Simplify the left side.

Cancel the common factor of $r^{2}$ .

Cancel the common factor.

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

Rewrite the expression.

$g m n = - f r^{2}$

Step 5

Divide each term in $g m n = - f r^{2}$ by $g n$ and simplify.

Divide each term in $g m n = - f r^{2}$ by $g n$ .

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

Simplify the left side.

Cancel the common factor of $g$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $n$ .

Cancel the common factor.

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

Divide $m$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Solve for m f=-(gmn)/(r^2)

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