Solve for z y=2wz-2wx-2xz

$y = 2 w z - 2 w x - 2 x z$

Step 1

Rewrite the equation as $2 w z - 2 w x - 2 x z = y$ .

$2 w z - 2 w x - 2 x z = y$

Step 2

Add $2 w x$ to both sides of the equation.

$2 w z - 2 x z = y + 2 w x$

Step 3

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

Factor $2 z$ out of $2 w z$ .

$2 z (w) - 2 x z = y + 2 w x$

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

$2 z (w) + 2 z (- x) = y + 2 w x$

Factor $2 z$ out of $2 z (w) + 2 z (- x)$ .

$2 z (w - x) = y + 2 w x$

Step 4

Divide each term in $2 z (w - x) = y + 2 w x$ by $2 (w - x)$ and simplify.

Divide each term in $2 z (w - x) = y + 2 w x$ by $2 (w - x)$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $w - x$ .

Cancel the common factor.

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

Divide $z$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

To write $\frac{w x}{w - x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$z = \frac{y}{2 (w - x)} + \frac{w x}{w - x} \cdot \frac{2}{2}$

Write each expression with a common denominator of $2 (w - x)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{w x}{w - x}$ by $\frac{2}{2}$ .

$z = \frac{y}{2 (w - x)} + \frac{w x \cdot 2}{(w - x) \cdot 2}$

Reorder the factors of $(w - x) \cdot 2$ .

$z = \frac{y}{2 (w - x)} + \frac{w x \cdot 2}{2 (w - x)}$

Combine the numerators over the common denominator.

$z = \frac{y + w x \cdot 2}{2 (w - x)}$

Move $2$ to the left of $w x$ .

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

Solve for z y=2wz-2wx-2xz

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