Solve for y 3xy+x=y-6

$3 x y + x = y - 6$

Subtract $y$ from both sides of the equation.

$3 x y + x - y = - 6$

Subtract $x$ from both sides of the equation.

$3 x y - y = - 6 - x$

Factor $y$ out of $3 x y - y$ .

Factor $y$ out of $3 x y$ .

$y (3 x) - y = - 6 - x$

Factor $y$ out of $- y$ .

$y (3 x) + y \cdot - 1 = - 6 - x$

Factor $y$ out of $y (3 x) + y \cdot - 1$ .

$y (3 x - 1) = - 6 - x$

Divide each term in $y (3 x - 1) = - 6 - x$ by $3 x - 1$ and simplify.

Divide each term in $y (3 x - 1) = - 6 - x$ by $3 x - 1$ .

$\frac{y (3 x - 1)}{3 x - 1} = \frac{- 6}{3 x - 1} + \frac{- x}{3 x - 1}$

Simplify the left side.

Cancel the common factor of $3 x - 1$ .

Cancel the common factor.

$\frac{y (3 x - 1)}{3 x - 1} = \frac{- 6}{3 x - 1} + \frac{- x}{3 x - 1}$

Divide $y$ by $1$ .

$y = \frac{- 6}{3 x - 1} + \frac{- x}{3 x - 1}$

Simplify the right side.

Combine the numerators over the common denominator.

$y = \frac{- 6 - x}{3 x - 1}$

Rewrite $- 6$ as $- 1 (6)$ .

$y = \frac{- 1 (6) - x}{3 x - 1}$

Factor $- 1$ out of $- x$ .

$y = \frac{- 1 (6) - (x)}{3 x - 1}$

Factor $- 1$ out of $- 1 (6) - (x)$ .

$y = \frac{- 1 (6 + x)}{3 x - 1}$

Move the negative in front of the fraction.

$y = - \frac{6 + x}{3 x - 1}$