Solve for X W=2yZ+2yX+2ZX

$W = 2 y Z + 2 y X + 2 Z X$

Step 1

Rewrite the equation as $2 y Z + 2 y X + 2 Z X = W$ .

$2 y Z + 2 y X + 2 Z X = W$

Step 2

Subtract $2 y Z$ from both sides of the equation.

$2 y X + 2 Z X = W - 2 y Z$

Step 3

Factor $2 X$ out of $2 y X + 2 Z X$ .

Factor $2 X$ out of $2 y X$ .

$2 X (y) + 2 Z X = W - 2 y Z$

Factor $2 X$ out of $2 Z X$ .

$2 X (y) + 2 X (Z) = W - 2 y Z$

Factor $2 X$ out of $2 X (y) + 2 X (Z)$ .

$2 X (y + Z) = W - 2 y Z$

Step 4

Divide each term in $2 X (y + Z) = W - 2 y Z$ by $2 (y + Z)$ and simplify.

Divide each term in $2 X (y + Z) = W - 2 y Z$ by $2 (y + Z)$ .

$\frac{2 X (y + Z)}{2 (y + Z)} = \frac{W}{2 (y + Z)} + \frac{- 2 y Z}{2 (y + Z)}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 X (y + Z)}{2 (y + Z)} = \frac{W}{2 (y + Z)} + \frac{- 2 y Z}{2 (y + Z)}$

Rewrite the expression.

$\frac{X (y + Z)}{y + Z} = \frac{W}{2 (y + Z)} + \frac{- 2 y Z}{2 (y + Z)}$

Cancel the common factor of $y + Z$ .

Cancel the common factor.

$\frac{X (y + Z)}{y + Z} = \frac{W}{2 (y + Z)} + \frac{- 2 y Z}{2 (y + Z)}$

Divide $X$ by $1$ .

$X = \frac{W}{2 (y + Z)} + \frac{- 2 y Z}{2 (y + Z)}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 2$ and $2$ .

Factor $2$ out of $- 2 y Z$ .

$X = \frac{W}{2 (y + Z)} + \frac{2 (- y Z)}{2 (y + Z)}$

Cancel the common factors.

Cancel the common factor.

$X = \frac{W}{2 (y + Z)} + \frac{2 (- y Z)}{2 (y + Z)}$

Rewrite the expression.

$X = \frac{W}{2 (y + Z)} + \frac{- y Z}{y + Z}$

Move the negative in front of the fraction.

$X = \frac{W}{2 (y + Z)} - \frac{y Z}{y + Z}$

To write $- \frac{y Z}{y + Z}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$X = \frac{W}{2 (y + Z)} - \frac{y Z}{y + Z} \cdot \frac{2}{2}$

Write each expression with a common denominator of $2 (y + Z)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{y Z}{y + Z}$ by $\frac{2}{2}$ .

$X = \frac{W}{2 (y + Z)} - \frac{y Z \cdot 2}{(y + Z) \cdot 2}$

Reorder the factors of $(y + Z) \cdot 2$ .

$X = \frac{W}{2 (y + Z)} - \frac{y Z \cdot 2}{2 (y + Z)}$

Combine the numerators over the common denominator.

$X = \frac{W - y Z \cdot 2}{2 (y + Z)}$

Multiply $2$ by $- 1$ .

$X = \frac{W - 2 y Z}{2 (y + Z)}$

Solve for X W=2yZ+2yX+2ZX

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