Solve -cz+6z=tz+83

$$- c z + 6 z = t z + 83$$

Solve for c

$$c=-t+6-\frac{83}{z}$$

$$z\neq 0$$

Steps for Solving Linear Equation

Subtract 6z from both sides.

$$\left(-c\right)z=tz+83-6z$$

Reorder the terms.

$$-cz=tz-6z+83$$

The equation is in standard form.

$$\left(-z\right)c=tz-6z+83$$

Divide both sides by -z.

$$\frac{\left(-z\right)c}{-z}=\frac{tz-6z+83}{-z}$$

Dividing by -z undoes the multiplication by -z.

$$c=\frac{tz-6z+83}{-z}$$

Divide tz-6z+83 by -z.

$$c=-t+6-\frac{83}{z}$$

Solve for t

$$t=-c+6-\frac{83}{z}$$

$$z\neq 0$$

Steps for Solving Linear Equation

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

$$tz+83=\left(-c\right)z+6z$$

Subtract 83 from both sides.

$$tz=\left(-c\right)z+6z-83$$

Reorder the terms.

$$tz=-cz+6z-83$$

The equation is in standard form.

$$zt=-cz+6z-83$$

Divide both sides by z.

$$\frac{zt}{z}=\frac{-cz+6z-83}{z}$$

Dividing by z undoes the multiplication by z.

$$t=\frac{-cz+6z-83}{z}$$

Divide -cz+6z-83 by z.

$$t=-c+6-\frac{83}{z}$$