Solve 3*CD=AD^2-AC^2

$$3 \times C D = A D ^ { 2 } - A C ^ { 2 }$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=-\frac{3CD}{C^{2}-D^{2}}\text{, }&C\neq -D\text{ and }C\neq D\\A\in \mathrm{C}\text{, }&D=0\text{ and }C=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$AD^{2}-AC^{2}=3CD$$

Reorder the terms.

$$-AC^{2}+AD^{2}=3CD$$

Combine all terms containing A.

$$\left(-C^{2}+D^{2}\right)A=3CD$$

The equation is in standard form.

$$\left(D^{2}-C^{2}\right)A=3CD$$

Divide both sides by -C^{2}+D^{2}.

$$\frac{\left(D^{2}-C^{2}\right)A}{D^{2}-C^{2}}=\frac{3CD}{D^{2}-C^{2}}$$

Dividing by -C^{2}+D^{2} undoes the multiplication by -C^{2}+D^{2}.

$$A=\frac{3CD}{D^{2}-C^{2}}$$

Solve for A

$$\left\{\begin{matrix}A=-\frac{3CD}{C^{2}-D^{2}}\text{, }&|C|\neq |D|\\A\in \mathrm{R}\text{, }&D=0\text{ and }C=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$AD^{2}-AC^{2}=3CD$$

Reorder the terms.

$$-AC^{2}+AD^{2}=3CD$$

Combine all terms containing A.

$$\left(-C^{2}+D^{2}\right)A=3CD$$

The equation is in standard form.

$$\left(D^{2}-C^{2}\right)A=3CD$$

Divide both sides by -C^{2}+D^{2}.

$$\frac{\left(D^{2}-C^{2}\right)A}{D^{2}-C^{2}}=\frac{3CD}{D^{2}-C^{2}}$$

Dividing by -C^{2}+D^{2} undoes the multiplication by -C^{2}+D^{2}.

$$A=\frac{3CD}{D^{2}-C^{2}}$$

Solve for C (complex solution)

$$\left\{\begin{matrix}C=\frac{\sqrt{D^{2}\left(4A^{2}+9\right)}-3D}{2A}\text{; }C=-\frac{\sqrt{D^{2}\left(4A^{2}+9\right)}+3D}{2A}\text{, }&A\neq 0\\C=0\text{, }&A=0\text{ and }D\neq 0\\C\in \mathrm{C}\text{, }&A=0\text{ and }D=0\end{matrix}\right.$$

Solve for C

$$\left\{\begin{matrix}C=\frac{D\left(\sqrt{4A^{2}+9}-3\right)}{2A}\text{; }C=-\frac{D\left(\sqrt{4A^{2}+9}+3\right)}{2A}\text{, }&A\neq 0\\C=0\text{, }&A=0\text{ and }D\neq 0\\C\in \mathrm{R}\text{, }&A=0\text{ and }D=0\end{matrix}\right.$$