Solve t+xy=varepsilon-xh

$$t + x y = \varepsilon - x h$$

Solve for h (complex solution)

$$\left\{\begin{matrix}h=\frac{-xy+\epsilon -t}{x}\text{, }&x\neq 0\\h\in \mathrm{C}\text{, }&t=\epsilon \text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\epsilon -xh=t+xy$$

Subtract \epsilon from both sides.

$$-xh=t+xy-\epsilon$$

The equation is in standard form.

$$\left(-x\right)h=xy+t-\epsilon$$

Divide both sides by -x.

$$\frac{\left(-x\right)h}{-x}=\frac{xy+t-\epsilon }{-x}$$

Dividing by -x undoes the multiplication by -x.

$$h=\frac{xy+t-\epsilon }{-x}$$

Divide t+xy-\epsilon by -x.

$$h=-\frac{xy+t-\epsilon }{x}$$

Solve for h

$$\left\{\begin{matrix}h=\frac{-xy+\epsilon -t}{x}\text{, }&x\neq 0\\h\in \mathrm{R}\text{, }&t=\epsilon \text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\epsilon -xh=t+xy$$

Subtract \epsilon from both sides.

$$-xh=t+xy-\epsilon$$

The equation is in standard form.

$$\left(-x\right)h=xy+t-\epsilon$$

Divide both sides by -x.

$$\frac{\left(-x\right)h}{-x}=\frac{xy+t-\epsilon }{-x}$$

Dividing by -x undoes the multiplication by -x.

$$h=\frac{xy+t-\epsilon }{-x}$$

Divide t+xy-\epsilon by -x.

$$h=-\frac{xy+t-\epsilon }{x}$$

Solve for t

$$t=\epsilon -xy-hx$$