Solve for x 3xy-2x+4y=100

$3 x y - 2 x + 4 y = 100$

Subtract $4 y$ from both sides of the equation.

$3 x y - 2 x = 100 - 4 y$

Factor $x$ out of $3 x y - 2 x$ .

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

$x (3 y) - 2 x = 100 - 4 y$

Factor $x$ out of $- 2 x$ .

$x (3 y) + x \cdot - 2 = 100 - 4 y$

Factor $x$ out of $x (3 y) + x \cdot - 2$ .

$x (3 y - 2) = 100 - 4 y$

Divide each term in $x (3 y - 2) = 100 - 4 y$ by $3 y - 2$ and simplify.

Divide each term in $x (3 y - 2) = 100 - 4 y$ by $3 y - 2$ .

$\frac{x (3 y - 2)}{3 y - 2} = \frac{100}{3 y - 2} + \frac{- 4 y}{3 y - 2}$

Simplify the left side.

Cancel the common factor of $3 y - 2$ .

Cancel the common factor.

$\frac{x (3 y - 2)}{3 y - 2} = \frac{100}{3 y - 2} + \frac{- 4 y}{3 y - 2}$

Divide $x$ by $1$ .

$x = \frac{100}{3 y - 2} + \frac{- 4 y}{3 y - 2}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{100 - 4 y}{3 y - 2}$

Factor $4$ out of $100 - 4 y$ .

Factor $4$ out of $100$ .

$x = \frac{4 (25) - 4 y}{3 y - 2}$

Factor $4$ out of $- 4 y$ .

$x = \frac{4 (25) + 4 (- y)}{3 y - 2}$

Factor $4$ out of $4 (25) + 4 (- y)$ .

$x = \frac{4 (25 - y)}{3 y - 2}$