Solve H=uaz-bTz

$$H = u a z - b T z$$

Solve for T

$$\left\{\begin{matrix}T=\frac{auz-H}{bz}\text{, }&z\neq 0\text{ and }b\neq 0\\T\in \mathrm{R}\text{, }&\left(H=auz\text{ and }b=0\right)\text{ or }\left(H=0\text{ and }z=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$uaz-bTz=H$$

Subtract uaz from both sides.

$$-bTz=H-uaz$$

The equation is in standard form.

$$\left(-bz\right)T=H-auz$$

Divide both sides by -bz.

$$\frac{\left(-bz\right)T}{-bz}=\frac{H-auz}{-bz}$$

Dividing by -bz undoes the multiplication by -bz.

$$T=\frac{H-auz}{-bz}$$

Divide H-uaz by -bz.

$$T=-\frac{H-auz}{bz}$$

Solve for H

$$H=z\left(au-Tb\right)$$