Solve for n 3n-5p+2n=10p for n

$3 n - 5 p + 2 n = 10 p$ for $n$

Add $3 n$ and $2 n$ .

$5 n - 5 p = 10 p$

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

Add $5 p$ to both sides of the equation.

$5 n = 10 p + 5 p$

Add $10 p$ and $5 p$ .

$5 n = 15 p$

Divide each term in $5 n = 15 p$ by $5$ and simplify.

Divide each term in $5 n = 15 p$ by $5$ .

$\frac{5 n}{5} = \frac{15 p}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 n}{5} = \frac{15 p}{5}$

Divide $n$ by $1$ .

$n = \frac{15 p}{5}$

Simplify the right side.

Cancel the common factor of $15$ and $5$ .

Factor $5$ out of $15 p$ .

$n = \frac{5 (3 p)}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

$n = \frac{5 (3 p)}{5 (1)}$

Cancel the common factor.

$n = \frac{5 (3 p)}{5 \cdot 1}$

Rewrite the expression.

$n = \frac{3 p}{1}$

Divide $3 p$ by $1$ .

$n = 3 p$