Solve for x y=2xz^2-xy

$y = 2 x z^{2} - x y$

Step 1

Rewrite the equation as $2 x z^{2} - x y = y$ .

$2 x z^{2} - x y = y$

Step 2

Factor $x$ out of $2 x z^{2} - x y$ .

Factor $x$ out of $2 x z^{2}$ .

$x (2 z^{2}) - x y = y$

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

$x (2 z^{2}) + x (- 1 y) = y$

Factor $x$ out of $x (2 z^{2}) + x (- 1 y)$ .

$x (2 z^{2} - 1 y) = y$

Step 3

Rewrite $- 1 y$ as $- y$ .

$x (2 z^{2} - y) = y$

Step 4

Divide each term in $x (2 z^{2} - y) = y$ by $2 z^{2} - y$ and simplify.

Divide each term in $x (2 z^{2} - y) = y$ by $2 z^{2} - y$ .

$\frac{x (2 z^{2} - y)}{2 z^{2} - y} = \frac{y}{2 z^{2} - y}$

Simplify the left side.

Cancel the common factor of $2 z^{2} - y$ .

Cancel the common factor.

$\frac{x (2 z^{2} - y)}{2 z^{2} - y} = \frac{y}{2 z^{2} - y}$

Divide $x$ by $1$ .

$x = \frac{y}{2 z^{2} - y}$