Solve for n 0.5n=1.5(-3n+10)

$0.5 n = 1.5 (- 3 n + 10)$

Simplify $1.5 (- 3 n + 10)$ .

Apply the distributive property.

$0.5 n = 1.5 (- 3 n) + 1.5 \cdot 10$

Multiply.

Multiply $- 3$ by $1.5$ .

$0.5 n = - 4.5 n + 1.5 \cdot 10$

Multiply $1.5$ by $10$ .

$0.5 n = - 4.5 n + 15$

Move all terms containing $n$ to the left side of the equation.

Add $4.5 n$ to both sides of the equation.

$0.5 n + 4.5 n = 15$

Add $0.5 n$ and $4.5 n$ .

$5 n = 15$

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

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

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $n$ by $1$ .

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

Simplify the right side.

Divide $15$ by $5$ .

$n = 3$