Solve for n 4n+2=10(1/5n-1)

$4 n + 2 = 10 (\frac{1}{5} n - 1)$

Step 1

Simplify $10 (\frac{1}{5} n - 1)$ .

Rewrite.

$4 n + 2 = 0 + 0 + 10 (\frac{1}{5} n - 1)$

Simplify by adding zeros.

$4 n + 2 = 10 (\frac{1}{5} n - 1)$

Combine $\frac{1}{5}$ and $n$ .

$4 n + 2 = 10 (\frac{n}{5} - 1)$

Apply the distributive property.

$4 n + 2 = 10 \frac{n}{5} + 10 \cdot - 1$

Cancel the common factor of $5$ .

Factor $5$ out of $10$ .

$4 n + 2 = 5 (2) \frac{n}{5} + 10 \cdot - 1$

Cancel the common factor.

$4 n + 2 = 5 \cdot 2 \frac{n}{5} + 10 \cdot - 1$

Rewrite the expression.

$4 n + 2 = 2 n + 10 \cdot - 1$

Multiply $10$ by $- 1$ .

$4 n + 2 = 2 n - 10$

Step 2

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

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

$4 n + 2 - 2 n = - 10$

Subtract $2 n$ from $4 n$ .

$2 n + 2 = - 10$

Step 3

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

Subtract $2$ from both sides of the equation.

$2 n = - 10 - 2$

Subtract $2$ from $- 10$ .

$2 n = - 12$

Step 4

Divide each term in $2 n = - 12$ by $2$ and simplify.

Divide each term in $2 n = - 12$ by $2$ .

$\frac{2 n}{2} = \frac{- 12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 n}{2} = \frac{- 12}{2}$

Divide $n$ by $1$ .

$n = \frac{- 12}{2}$

Simplify the right side.

Divide $- 12$ by $2$ .

$n = - 6$