Solve for n 4(0.5n-3)=n-0.25(12-8n)

$4 (0.5 n - 3) = n - 0.25 (12 - 8 n)$

Step 1

Since $n$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$n - 0.25 (12 - 8 n) = 4 (0.5 n - 3)$

Step 2

Simplify $n - 0.25 (12 - 8 n)$ .

Simplify each term.

Apply the distributive property.

$n - 0.25 \cdot 12 - 0.25 (- 8 n) = 4 (0.5 n - 3)$

Multiply $- 0.25$ by $12$ .

$n - 3 - 0.25 (- 8 n) = 4 (0.5 n - 3)$

Multiply $- 8$ by $- 0.25$ .

$n - 3 + 2 n = 4 (0.5 n - 3)$

Add $n$ and $2 n$ .

$3 n - 3 = 4 (0.5 n - 3)$

Step 3

Simplify $4 (0.5 n - 3)$ .

Apply the distributive property.

$3 n - 3 = 4 (0.5 n) + 4 \cdot - 3$

Multiply.

Multiply $0.5$ by $4$ .

$3 n - 3 = 2 n + 4 \cdot - 3$

Multiply $4$ by $- 3$ .

$3 n - 3 = 2 n - 12$

Step 4

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

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

$3 n - 3 - 2 n = - 12$

Subtract $2 n$ from $3 n$ .

$n - 3 = - 12$

Step 5

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

Add $3$ to both sides of the equation.

$n = - 12 + 3$

Add $- 12$ and $3$ .

$n = - 9$