Solve for n 4n-40=7(-2n+2)

$4 n - 40 = 7 (- 2 n + 2)$

Step 1

Simplify $7 (- 2 n + 2)$ .

Rewrite.

$4 n - 40 = 0 + 0 + 7 (- 2 n + 2)$

Simplify by adding zeros.

$4 n - 40 = 7 (- 2 n + 2)$

Apply the distributive property.

$4 n - 40 = 7 (- 2 n) + 7 \cdot 2$

Multiply.

Multiply $- 2$ by $7$ .

$4 n - 40 = - 14 n + 7 \cdot 2$

Multiply $7$ by $2$ .

$4 n - 40 = - 14 n + 14$

Step 2

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

Add $14 n$ to both sides of the equation.

$4 n - 40 + 14 n = 14$

Add $4 n$ and $14 n$ .

$18 n - 40 = 14$

Step 3

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

Add $40$ to both sides of the equation.

$18 n = 14 + 40$

Add $14$ and $40$ .

$18 n = 54$

Step 4

Divide each term in $18 n = 54$ by $18$ and simplify.

Divide each term in $18 n = 54$ by $18$ .

$\frac{18 n}{18} = \frac{54}{18}$

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 n}{18} = \frac{54}{18}$

Divide $n$ by $1$ .

$n = \frac{54}{18}$

Simplify the right side.

Divide $54$ by $18$ .

$n = 3$