Solve DE*BE=CE*TE

$$DE \times BE = CE \times TE$$

Solve for B

$$\left\{\begin{matrix}B=\frac{CT}{D}\text{, }&D\neq 0\\B\in \mathrm{R}\text{, }&E=0\text{ or }\left(C=0\text{ and }D=0\right)\text{ or }\left(T=0\text{ and }D=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply E and E to get E^{2}.

$$DE^{2}B=CETE$$

Multiply E and E to get E^{2}.

$$DE^{2}B=CE^{2}T$$

The equation is in standard form.

$$DE^{2}B=CTE^{2}$$

Divide both sides by DE^{2}.

$$\frac{DE^{2}B}{DE^{2}}=\frac{CTE^{2}}{DE^{2}}$$

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

$$B=\frac{CTE^{2}}{DE^{2}}$$

Divide CE^{2}T by DE^{2}.

$$B=\frac{CT}{D}$$

Solve for C

$$\left\{\begin{matrix}C=\frac{BD}{T}\text{, }&T\neq 0\\C\in \mathrm{R}\text{, }&E=0\text{ or }\left(D=0\text{ and }T=0\right)\text{ or }\left(B=0\text{ and }T=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply E and E to get E^{2}.

$$DE^{2}B=CETE$$

Multiply E and E to get E^{2}.

$$DE^{2}B=CE^{2}T$$

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

$$CE^{2}T=DE^{2}B$$

The equation is in standard form.

$$TE^{2}C=BDE^{2}$$

Divide both sides by E^{2}T.

$$\frac{TE^{2}C}{TE^{2}}=\frac{BDE^{2}}{TE^{2}}$$

Dividing by E^{2}T undoes the multiplication by E^{2}T.

$$C=\frac{BDE^{2}}{TE^{2}}$$

Divide DE^{2}B by E^{2}T.

$$C=\frac{BD}{T}$$