Solve w_{2}-x(y-t_{x})=(w+1)y

$$w _ { 2 } - x ( y - t _ { x } ) = ( w + 1 ) y$$

Solve for t_x (complex solution)

$$\left\{\begin{matrix}t_{x}=\frac{xy+wy+y-w_{2}}{x}\text{, }&x\neq 0\\t_{x}\in \mathrm{C}\text{, }&w_{2}=wy+y\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by y-t_{x}.

$$w_{2}-\left(xy-xt_{x}\right)=\left(w+1\right)y$$

To find the opposite of xy-xt_{x}, find the opposite of each term.

$$w_{2}-xy+xt_{x}=\left(w+1\right)y$$

Use the distributive property to multiply w+1 by y.

$$w_{2}-xy+xt_{x}=wy+y$$

Subtract w_{2} from both sides.

$$-xy+xt_{x}=wy+y-w_{2}$$

Add xy to both sides.

$$xt_{x}=wy+y-w_{2}+xy$$

The equation is in standard form.

$$xt_{x}=xy+wy+y-w_{2}$$

Divide both sides by x.

$$\frac{xt_{x}}{x}=\frac{xy+wy+y-w_{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$t_{x}=\frac{xy+wy+y-w_{2}}{x}$$

Solve for w (complex solution)

$$\left\{\begin{matrix}w=\frac{t_{x}x-xy-y+w_{2}}{y}\text{, }&y\neq 0\\w\in \mathrm{C}\text{, }&w_{2}=-t_{x}x\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by y-t_{x}.

$$w_{2}-\left(xy-xt_{x}\right)=\left(w+1\right)y$$

To find the opposite of xy-xt_{x}, find the opposite of each term.

$$w_{2}-xy+xt_{x}=\left(w+1\right)y$$

Use the distributive property to multiply w+1 by y.

$$w_{2}-xy+xt_{x}=wy+y$$

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

$$wy+y=w_{2}-xy+xt_{x}$$

Subtract y from both sides.

$$wy=w_{2}-xy+xt_{x}-y$$

The equation is in standard form.

$$yw=t_{x}x-xy-y+w_{2}$$

Divide both sides by y.

$$\frac{yw}{y}=\frac{t_{x}x-xy-y+w_{2}}{y}$$

Dividing by y undoes the multiplication by y.

$$w=\frac{t_{x}x-xy-y+w_{2}}{y}$$

Solve for t_x

$$\left\{\begin{matrix}t_{x}=\frac{xy+wy+y-w_{2}}{x}\text{, }&x\neq 0\\t_{x}\in \mathrm{R}\text{, }&w_{2}=wy+y\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by y-t_{x}.

$$w_{2}-\left(xy-xt_{x}\right)=\left(w+1\right)y$$

To find the opposite of xy-xt_{x}, find the opposite of each term.

$$w_{2}-xy+xt_{x}=\left(w+1\right)y$$

Use the distributive property to multiply w+1 by y.

$$w_{2}-xy+xt_{x}=wy+y$$

Subtract w_{2} from both sides.

$$-xy+xt_{x}=wy+y-w_{2}$$

Add xy to both sides.

$$xt_{x}=wy+y-w_{2}+xy$$

The equation is in standard form.

$$xt_{x}=xy+wy+y-w_{2}$$

Divide both sides by x.

$$\frac{xt_{x}}{x}=\frac{xy+wy+y-w_{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$t_{x}=\frac{xy+wy+y-w_{2}}{x}$$

Solve for w

$$\left\{\begin{matrix}w=\frac{t_{x}x-xy-y+w_{2}}{y}\text{, }&y\neq 0\\w\in \mathrm{R}\text{, }&w_{2}=-t_{x}x\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by y-t_{x}.

$$w_{2}-\left(xy-xt_{x}\right)=\left(w+1\right)y$$

To find the opposite of xy-xt_{x}, find the opposite of each term.

$$w_{2}-xy+xt_{x}=\left(w+1\right)y$$

Use the distributive property to multiply w+1 by y.

$$w_{2}-xy+xt_{x}=wy+y$$

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

$$wy+y=w_{2}-xy+xt_{x}$$

Subtract y from both sides.

$$wy=w_{2}-xy+xt_{x}-y$$

The equation is in standard form.

$$yw=t_{x}x-xy-y+w_{2}$$

Divide both sides by y.

$$\frac{yw}{y}=\frac{t_{x}x-xy-y+w_{2}}{y}$$

Dividing by y undoes the multiplication by y.

$$w=\frac{t_{x}x-xy-y+w_{2}}{y}$$