Solve for n 150=(180(n-2))/n

$150 = \frac{180 (n - 2)}{n}$

Rewrite the equation as $\frac{180 (n - 2)}{n} = 150$ .

$\frac{180 (n - 2)}{n} = 150$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$n, 1$

The LCM of one and any expression is the expression.

$n$

Multiply each term in $\frac{180 (n - 2)}{n} = 150$ by $n$ to eliminate the fractions.

Multiply each term in $\frac{180 (n - 2)}{n} = 150$ by $n$ .

$\frac{180 (n - 2)}{n} n = 150 n$

Simplify the left side.

Cancel the common factor of $n$ .

Cancel the common factor.

$\frac{180 (n - 2)}{n} n = 150 n$

Rewrite the expression.

$180 (n - 2) = 150 n$

Apply the distributive property.

$180 n + 180 \cdot - 2 = 150 n$

Multiply $180$ by $- 2$ .

$180 n - 360 = 150 n$

Solve the equation.

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

Subtract $150 n$ from both sides of the equation.

$180 n - 360 - 150 n = 0$

Subtract $150 n$ from $180 n$ .

$30 n - 360 = 0$

Add $360$ to both sides of the equation.

$30 n = 360$

Divide each term in $30 n = 360$ by $30$ and simplify.

Divide each term in $30 n = 360$ by $30$ .

$\frac{30 n}{30} = \frac{360}{30}$

Simplify the left side.

Cancel the common factor of $30$ .

Cancel the common factor.

$\frac{30 n}{30} = \frac{360}{30}$

Divide $n$ by $1$ .

$n = \frac{360}{30}$

Simplify the right side.

Divide $360$ by $30$ .

$n = 12$