Solve for x 3xy+x=y-6

$3 x y + x = y - 6$

Step 1

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

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

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

Raise $x$ to the power of $1$ .

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

Factor $x$ out of $x^{1}$ .

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

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

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

Step 2

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

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

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

Simplify the left side.

Cancel the common factor of $3 y + 1$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Combine the numerators over the common denominator.

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