Solve for n n-2=(10n+4)/2

$n - 2 = \frac{10 n + 4}{2}$

Step 1

Cancel the common factor of $10 n + 4$ and $2$ .

Factor $2$ out of $10 n$ .

$n - 2 = \frac{2 (5 n) + 4}{2}$

Factor $2$ out of $4$ .

$n - 2 = \frac{2 (5 n) + 2 \cdot 2}{2}$

Factor $2$ out of $2 (5 n) + 2 (2)$ .

$n - 2 = \frac{2 (5 n + 2)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$n - 2 = \frac{2 (5 n + 2)}{2 (1)}$

Cancel the common factor.

$n - 2 = \frac{2 (5 n + 2)}{2 \cdot 1}$

Rewrite the expression.

$n - 2 = \frac{5 n + 2}{1}$

Divide $5 n + 2$ by $1$ .

$n - 2 = 5 n + 2$

Step 2

Solve for $n$ .

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

Subtract $5 n$ from both sides of the equation.

$n - 2 - 5 n = 2$

Subtract $5 n$ from $n$ .

$- 4 n - 2 = 2$

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

Add $2$ to both sides of the equation.

$- 4 n = 2 + 2$

Add $2$ and $2$ .

$- 4 n = 4$

Divide each term in $- 4 n = 4$ by $- 4$ and simplify.

Divide each term in $- 4 n = 4$ by $- 4$ .

$\frac{- 4 n}{- 4} = \frac{4}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 n}{- 4} = \frac{4}{- 4}$

Divide $n$ by $1$ .

$n = \frac{4}{- 4}$

Simplify the right side.

Divide $4$ by $- 4$ .

$n = - 1$