Solve for n (2m-n)/3=5m

$\frac{2 m - n}{3} = 5 m$

Step 1

Multiply both sides by $3$ .

$\frac{2 m - n}{3} \cdot 3 = 5 m \cdot 3$

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2 m - n}{3} \cdot 3 = 5 m \cdot 3$

Rewrite the expression.

$2 m - n = 5 m \cdot 3$

Simplify the right side.

Multiply $3$ by $5$ .

$2 m - n = 15 m$

Step 3

Solve for $n$ .

Move all terms not containing $n$ to the right side of the equation.

Subtract $2 m$ from both sides of the equation.

$- n = 15 m - 2 m$

Subtract $2 m$ from $15 m$ .

$- n = 13 m$

Divide each term in $- n = 13 m$ by $- 1$ and simplify.

Divide each term in $- n = 13 m$ by $- 1$ .

$\frac{- n}{- 1} = \frac{13 m}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{n}{1} = \frac{13 m}{- 1}$

Divide $n$ by $1$ .

$n = \frac{13 m}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{13 m}{- 1}$ .

$n = - 1 \cdot (13 m)$

Rewrite $- 1 \cdot (13 m)$ as $- (13 m)$ .

$n = - (13 m)$

Multiply $13$ by $- 1$ .

$n = - 13 m$