Solve zyleft(1+2xright)+left(1-zright)x2y=0y=

$$zy \left( 1+2x \right) + \left( 1-z \right) x2y = 0y=$$

Solve for x

$$\left\{\begin{matrix}x=\frac{x_{2}}{2}-\frac{x_{2}}{2z}-\frac{1}{2}\text{, }&z\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ or }\left(x_{2}=0\text{ and }z=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply zy by 1+2x.

$$zy+2zyx+\left(1-z\right)x_{2}y=0y$$

Use the distributive property to multiply 1-z by x_{2}.

$$zy+2zyx+\left(x_{2}-zx_{2}\right)y=0y$$

Use the distributive property to multiply x_{2}-zx_{2} by y.

$$zy+2zyx+x_{2}y-zx_{2}y=0y$$

Anything times zero gives zero.

$$zy+2zyx+x_{2}y-zx_{2}y=0$$

Subtract zy from both sides. Anything subtracted from zero gives its negation.

$$2zyx+x_{2}y-zx_{2}y=-zy$$

Subtract x_{2}y from both sides.

$$2zyx-zx_{2}y=-zy-x_{2}y$$

Add zx_{2}y to both sides.

$$2zyx=-zy-x_{2}y+zx_{2}y$$

Reorder the terms.

$$2xyz=x_{2}yz-x_{2}y-yz$$

The equation is in standard form.

$$2yzx=x_{2}yz-x_{2}y-yz$$

Divide both sides by 2yz.

$$\frac{2yzx}{2yz}=\frac{y\left(x_{2}z-x_{2}-z\right)}{2yz}$$

Dividing by 2yz undoes the multiplication by 2yz.

$$x=\frac{y\left(x_{2}z-x_{2}-z\right)}{2yz}$$

Divide y\left(x_{2}z-x_{2}-z\right) by 2yz.

$$x=\frac{x_{2}}{2}-\frac{x_{2}}{2z}-\frac{1}{2}$$

Solve for x_2

$$\left\{\begin{matrix}x_{2}=-\frac{z\left(2x+1\right)}{1-z}\text{, }&z\neq 1\\x_{2}\in \mathrm{R}\text{, }&y=0\text{ or }\left(x=-\frac{1}{2}\text{ and }z=1\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply zy by 1+2x.

$$zy+2zyx+\left(1-z\right)x_{2}y=0y$$

Use the distributive property to multiply 1-z by x_{2}.

$$zy+2zyx+\left(x_{2}-zx_{2}\right)y=0y$$

Use the distributive property to multiply x_{2}-zx_{2} by y.

$$zy+2zyx+x_{2}y-zx_{2}y=0y$$

Anything times zero gives zero.

$$zy+2zyx+x_{2}y-zx_{2}y=0$$

Subtract zy from both sides. Anything subtracted from zero gives its negation.

$$2zyx+x_{2}y-zx_{2}y=-zy$$

Subtract 2zyx from both sides.

$$x_{2}y-zx_{2}y=-zy-2zyx$$

Reorder the terms.

$$-x_{2}yz+x_{2}y=-2xyz-yz$$

Combine all terms containing x_{2}.

$$\left(-yz+y\right)x_{2}=-2xyz-yz$$

The equation is in standard form.

$$\left(y-yz\right)x_{2}=-2xyz-yz$$

Divide both sides by -yz+y.

$$\frac{\left(y-yz\right)x_{2}}{y-yz}=-\frac{yz\left(2x+1\right)}{y-yz}$$

Dividing by -yz+y undoes the multiplication by -yz+y.

$$x_{2}=-\frac{yz\left(2x+1\right)}{y-yz}$$

Divide -zy\left(1+2x\right) by -yz+y.

$$x_{2}=-\frac{z\left(2x+1\right)}{1-z}$$