Solve w-xleft(y-txright)=left(w+1right)y

$$w-x \left( y-tx \right) = \left( w+1 \right) y$$

Solve for t (complex solution)

$$\left\{\begin{matrix}t=\frac{xy+wy+y-w}{x^{2}}\text{, }&x\neq 0\\t\in \mathrm{C}\text{, }&w=\frac{y}{1-y}\text{ and }y\neq 1\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by y-tx.

$$w-\left(xy-tx^{2}\right)=\left(w+1\right)y$$

To find the opposite of xy-tx^{2}, find the opposite of each term.

$$w-xy+tx^{2}=\left(w+1\right)y$$

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

$$w-xy+tx^{2}=wy+y$$

Subtract w from both sides.

$$-xy+tx^{2}=wy+y-w$$

Add xy to both sides.

$$tx^{2}=wy+y-w+xy$$

The equation is in standard form.

$$x^{2}t=xy+wy+y-w$$

Divide both sides by x^{2}.

$$\frac{x^{2}t}{x^{2}}=\frac{xy+wy+y-w}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$t=\frac{xy+wy+y-w}{x^{2}}$$

Solve for w (complex solution)

$$\left\{\begin{matrix}w=-\frac{tx^{2}-xy-y}{1-y}\text{, }&y\neq 1\\w\in \mathrm{C}\text{, }&\left(x=\frac{-\sqrt{4t+1}+1}{2t}\text{ and }y=1\text{ and }t\neq 0\right)\text{ or }\left(x=\frac{\sqrt{4t+1}+1}{2t}\text{ and }y=1\text{ and }t\neq 0\right)\text{ or }\left(t=0\text{ and }y=1\text{ and }x=-1\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by y-tx.

$$w-\left(xy-tx^{2}\right)=\left(w+1\right)y$$

To find the opposite of xy-tx^{2}, find the opposite of each term.

$$w-xy+tx^{2}=\left(w+1\right)y$$

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

$$w-xy+tx^{2}=wy+y$$

Subtract wy from both sides.

$$w-xy+tx^{2}-wy=y$$

Add xy to both sides.

$$w+tx^{2}-wy=y+xy$$

Subtract tx^{2} from both sides.

$$w-wy=y+xy-tx^{2}$$

Reorder the terms.

$$-wy+w=-tx^{2}+xy+y$$

Combine all terms containing w.

$$\left(-y+1\right)w=-tx^{2}+xy+y$$

The equation is in standard form.

$$\left(1-y\right)w=y+xy-tx^{2}$$

Divide both sides by -y+1.

$$\frac{\left(1-y\right)w}{1-y}=\frac{y+xy-tx^{2}}{1-y}$$

Dividing by -y+1 undoes the multiplication by -y+1.

$$w=\frac{y+xy-tx^{2}}{1-y}$$

Solve for t

$$\left\{\begin{matrix}t=\frac{xy+wy+y-w}{x^{2}}\text{, }&x\neq 0\\t\in \mathrm{R}\text{, }&w=\frac{y}{1-y}\text{ and }y\neq 1\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by y-tx.

$$w-\left(xy-tx^{2}\right)=\left(w+1\right)y$$

To find the opposite of xy-tx^{2}, find the opposite of each term.

$$w-xy+tx^{2}=\left(w+1\right)y$$

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

$$w-xy+tx^{2}=wy+y$$

Subtract w from both sides.

$$-xy+tx^{2}=wy+y-w$$

Add xy to both sides.

$$tx^{2}=wy+y-w+xy$$

The equation is in standard form.

$$x^{2}t=xy+wy+y-w$$

Divide both sides by x^{2}.

$$\frac{x^{2}t}{x^{2}}=\frac{xy+wy+y-w}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$t=\frac{xy+wy+y-w}{x^{2}}$$

Solve for w

$$\left\{\begin{matrix}w=-\frac{tx^{2}-xy-y}{1-y}\text{, }&y\neq 1\\w\in \mathrm{R}\text{, }&\left(x=\frac{-\sqrt{4t+1}+1}{2t}\text{ and }y=1\text{ and }t\geq -\frac{1}{4}\text{ and }t\neq 0\right)\text{ or }\left(y=1\text{ and }t=-\frac{1}{4}\text{ and }x=-2\right)\text{ or }\left(x=\frac{\sqrt{4t+1}+1}{2t}\text{ and }y=1\text{ and }t\geq -\frac{1}{4}\text{ and }t\neq 0\right)\text{ or }\left(t=0\text{ and }y=1\text{ and }x=-1\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by y-tx.

$$w-\left(xy-tx^{2}\right)=\left(w+1\right)y$$

To find the opposite of xy-tx^{2}, find the opposite of each term.

$$w-xy+tx^{2}=\left(w+1\right)y$$

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

$$w-xy+tx^{2}=wy+y$$

Subtract wy from both sides.

$$w-xy+tx^{2}-wy=y$$

Add xy to both sides.

$$w+tx^{2}-wy=y+xy$$

Subtract tx^{2} from both sides.

$$w-wy=y+xy-tx^{2}$$

Reorder the terms.

$$-wy+w=-tx^{2}+xy+y$$

Combine all terms containing w.

$$\left(-y+1\right)w=-tx^{2}+xy+y$$

The equation is in standard form.

$$\left(1-y\right)w=y+xy-tx^{2}$$

Divide both sides by -y+1.

$$\frac{\left(1-y\right)w}{1-y}=\frac{y+xy-tx^{2}}{1-y}$$

Dividing by -y+1 undoes the multiplication by -y+1.

$$w=\frac{y+xy-tx^{2}}{1-y}$$