Solve Ax+3A^3/A^2+9=3A

$$A x + \frac { 3 A ^ { 3 } } { A ^ { 2 } + 9 } = 3 A$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{27}{A^{2}+9}\text{, }&A\neq -3i\text{ and }A\neq 3i\\x\in \mathrm{C}\text{, }&A=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(A-3i\right)\left(A+3i\right).

$$Ax\left(A-3i\right)\left(A+3i\right)+3A^{3}=3A\left(A-3i\right)\left(A+3i\right)$$

Use the distributive property to multiply Ax by A-3i.

$$\left(xA^{2}-3iAx\right)\left(A+3i\right)+3A^{3}=3A\left(A-3i\right)\left(A+3i\right)$$

Use the distributive property to multiply xA^{2}-3iAx by A+3i and combine like terms.

$$xA^{3}+9xA+3A^{3}=3A\left(A-3i\right)\left(A+3i\right)$$

Use the distributive property to multiply 3A by A-3i.

$$xA^{3}+9xA+3A^{3}=\left(3A^{2}-9iA\right)\left(A+3i\right)$$

Use the distributive property to multiply 3A^{2}-9iA by A+3i and combine like terms.

$$xA^{3}+9xA+3A^{3}=3A^{3}+27A$$

Subtract 3A^{3} from both sides.

$$xA^{3}+9xA=3A^{3}+27A-3A^{3}$$

Combine 3A^{3} and -3A^{3} to get 0.

$$xA^{3}+9xA=27A$$

Combine all terms containing x.

$$\left(A^{3}+9A\right)x=27A$$

Divide both sides by A^{3}+9A.

$$\frac{\left(A^{3}+9A\right)x}{A^{3}+9A}=\frac{27A}{A^{3}+9A}$$

Dividing by A^{3}+9A undoes the multiplication by A^{3}+9A.

$$x=\frac{27A}{A^{3}+9A}$$

Divide 27A by A^{3}+9A.

$$x=\frac{27}{A^{2}+9}$$

Solve for x

$$\left\{\begin{matrix}\\x=\frac{27}{A^{2}+9}\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&A=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by A^{2}+9.

$$Ax\left(A^{2}+9\right)+3A^{3}=3A\left(A^{2}+9\right)$$

Use the distributive property to multiply Ax by A^{2}+9.

$$xA^{3}+9Ax+3A^{3}=3A\left(A^{2}+9\right)$$

Use the distributive property to multiply 3A by A^{2}+9.

$$xA^{3}+9Ax+3A^{3}=3A^{3}+27A$$

Subtract 3A^{3} from both sides.

$$xA^{3}+9Ax=3A^{3}+27A-3A^{3}$$

Combine 3A^{3} and -3A^{3} to get 0.

$$xA^{3}+9Ax=27A$$

Combine all terms containing x.

$$\left(A^{3}+9A\right)x=27A$$

Divide both sides by A^{3}+9A.

$$\frac{\left(A^{3}+9A\right)x}{A^{3}+9A}=\frac{27A}{A^{3}+9A}$$

Dividing by A^{3}+9A undoes the multiplication by A^{3}+9A.

$$x=\frac{27A}{A^{3}+9A}$$

Divide 27A by A^{3}+9A.

$$x=\frac{27}{A^{2}+9}$$

Solve for A (complex solution)

$$\left\{\begin{matrix}\\A=0\text{, }&\text{unconditionally}\\A=-3\sqrt{-1+\frac{3}{x}}\text{; }A=3\sqrt{-1+\frac{3}{x}}\text{, }&x\neq 0\end{matrix}\right.$$

Solve for A

$$\left\{\begin{matrix}\\A=0\text{, }&\text{unconditionally}\\A=3\sqrt{-1+\frac{3}{x}}\text{; }A=-3\sqrt{-1+\frac{3}{x}}\text{, }&x>0\text{ and }x\leq 3\end{matrix}\right.$$