Solve W=2ZX+2ZY+2XY

$$W = 2 Z X + 2 Z Y + 2 X Y$$

Solve for X

$$\left\{\begin{matrix}X=-\frac{2YZ-W}{2\left(Y+Z\right)}\text{, }&Z\neq -Y\\X\in \mathrm{R}\text{, }&W=-2Y^{2}\text{ and }Z=-Y\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$2ZX+2ZY+2XY=W$$

Subtract 2ZY from both sides.

$$2ZX+2XY=W-2ZY$$

Combine all terms containing X.

$$\left(2Z+2Y\right)X=W-2ZY$$

The equation is in standard form.

$$\left(2Y+2Z\right)X=W-2YZ$$

Divide both sides by 2Z+2Y.

$$\frac{\left(2Y+2Z\right)X}{2Y+2Z}=\frac{W-2YZ}{2Y+2Z}$$

Dividing by 2Z+2Y undoes the multiplication by 2Z+2Y.

$$X=\frac{W-2YZ}{2Y+2Z}$$

Divide -2YZ+W by 2Z+2Y.

$$X=\frac{W-2YZ}{2\left(Y+Z\right)}$$

Solve for W

$$W=2\left(XY+XZ+YZ\right)$$