Solve operatorname{atim}(D^3+2D^2+D)=x^2

$$\operatorname { atim } ( D ^ { 3 } + 2 D ^ { 2 } + D ) = x ^ { 2 }$$

Solve for a

$$\left\{\begin{matrix}a=\frac{x^{2}}{t\left(Re(D)Im(\left(D+1\right)^{2})+Im(D)Re(\left(D+1\right)^{2})\right)}\text{, }&t\neq 0\text{ and }Re(D)Im(\left(D+1\right)^{2})+Im(D)Re(\left(D+1\right)^{2})\neq 0\\a\in \mathrm{C}\text{, }&\left(Re(D)Im(\left(D+1\right)^{2})+Im(D)Re(\left(D+1\right)^{2})=0\text{ or }t=0\right)\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$t\left(Im(D^{3})+2Im(D^{2})+Im(D)\right)a=x^{2}$$

Divide both sides by t\left(Im(D^{3})+2Im(D^{2})+Im(D)\right).

$$\frac{t\left(Im(D^{3})+2Im(D^{2})+Im(D)\right)a}{t\left(Im(D^{3})+2Im(D^{2})+Im(D)\right)}=\frac{x^{2}}{t\left(Im(D^{3})+2Im(D^{2})+Im(D)\right)}$$

Dividing by t\left(Im(D^{3})+2Im(D^{2})+Im(D)\right) undoes the multiplication by t\left(Im(D^{3})+2Im(D^{2})+Im(D)\right).

$$a=\frac{x^{2}}{t\left(Im(D^{3})+2Im(D^{2})+Im(D)\right)}$$