Solve for d N=3qd-rd

$N = 3 q d - r d$

Rewrite the equation as $3 q d - r d = N$ .

$3 q d - r d = N$

Factor $d$ out of $3 q d - r d$ .

Factor $d$ out of $3 q d$ .

$d (3 q) - r d = N$

Factor $d$ out of $- r d$ .

$d (3 q) + d (- r) = N$

Factor $d$ out of $d (3 q) + d (- r)$ .

$d (3 q - r) = N$

Divide each term in $d (3 q - r) = N$ by $3 q - r$ and simplify.

Divide each term in $d (3 q - r) = N$ by $3 q - r$ .

$\frac{d (3 q - r)}{3 q - r} = \frac{N}{3 q - r}$

Simplify the left side.

Cancel the common factor of $3 q - r$ .

Cancel the common factor.

$\frac{d (3 q - r)}{3 q - r} = \frac{N}{3 q - r}$

Divide $d$ by $1$ .

$d = \frac{N}{3 q - r}$