Solve operatorname{deg}p(x)=operatorname{deg}q(x)

$$\operatorname { deg } p ( x ) = \operatorname { deg } q ( x )$$

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&p=q\text{ or }x=0\text{ or }g=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out e on both sides.

$$dgpx=dgqx$$

Subtract dgqx from both sides.

$$dgpx-dgqx=0$$

Combine all terms containing d.

$$\left(gpx-gqx\right)d=0$$

Divide 0 by gpx-gqx.

$$d=0$$

Solve for g (complex solution)

$$\left\{\begin{matrix}\\g=0\text{, }&\text{unconditionally}\\g\in \mathrm{C}\text{, }&p=q\text{ or }x=0\text{ or }d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out e on both sides.

$$dgpx=dgqx$$

Subtract dgqx from both sides.

$$dgpx-dgqx=0$$

Combine all terms containing g.

$$\left(dpx-dqx\right)g=0$$

Divide 0 by dpx-dqx.

$$g=0$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&p=q\text{ or }x=0\text{ or }g=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out e on both sides.

$$dgpx=dgqx$$

Subtract dgqx from both sides.

$$dgpx-dgqx=0$$

Combine all terms containing d.

$$\left(gpx-gqx\right)d=0$$

Divide 0 by gpx-gqx.

$$d=0$$

Solve for g

$$\left\{\begin{matrix}\\g=0\text{, }&\text{unconditionally}\\g\in \mathrm{R}\text{, }&p=q\text{ or }x=0\text{ or }d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out e on both sides.

$$dgpx=dgqx$$

Subtract dgqx from both sides.

$$dgpx-dgqx=0$$

Combine all terms containing g.

$$\left(dpx-dqx\right)g=0$$

Divide 0 by dpx-dqx.

$$g=0$$