Solve for n 3an-2a+100=2a-50

$3 a n - 2 a + 100 = 2 a - 50$

Step 1

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

Add $2 a$ to both sides of the equation.

$3 a n + 100 = 2 a - 50 + 2 a$

Subtract $100$ from both sides of the equation.

$3 a n = 2 a - 50 + 2 a - 100$

Add $2 a$ and $2 a$ .

$3 a n = 4 a - 50 - 100$

Subtract $100$ from $- 50$ .

$3 a n = 4 a - 150$

Step 2

Divide each term in $3 a n = 4 a - 150$ by $3 a$ and simplify.

Divide each term in $3 a n = 4 a - 150$ by $3 a$ .

$\frac{3 a n}{3 a} = \frac{4 a}{3 a} + \frac{- 150}{3 a}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 a n}{3 a} = \frac{4 a}{3 a} + \frac{- 150}{3 a}$

Rewrite the expression.

$\frac{a n}{a} = \frac{4 a}{3 a} + \frac{- 150}{3 a}$

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{a n}{a} = \frac{4 a}{3 a} + \frac{- 150}{3 a}$

Divide $n$ by $1$ .

$n = \frac{4 a}{3 a} + \frac{- 150}{3 a}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $a$ .

Cancel the common factor.

$n = \frac{4 a}{3 a} + \frac{- 150}{3 a}$

Rewrite the expression.

$n = \frac{4}{3} + \frac{- 150}{3 a}$

Cancel the common factor of $- 150$ and $3$ .

Factor $3$ out of $- 150$ .

$n = \frac{4}{3} + \frac{3 \cdot - 50}{3 a}$

Cancel the common factors.

Factor $3$ out of $3 a$ .

$n = \frac{4}{3} + \frac{3 \cdot - 50}{3 (a)}$

Cancel the common factor.

$n = \frac{4}{3} + \frac{3 \cdot - 50}{3 a}$

Rewrite the expression.

$n = \frac{4}{3} + \frac{- 50}{a}$

Move the negative in front of the fraction.

$n = \frac{4}{3} - \frac{50}{a}$