Solve x^3-27=(x-3)A

$$x ^ { 3 } - 27 = ( x - 3 ) A$$

Solve for A (complex solution)

$$\left\{\begin{matrix}\\A=x^{2}+3x+9\text{, }&\text{unconditionally}\\A\in \mathrm{C}\text{, }&x=3\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x^{3}-27=xA-3A$$

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

$$xA-3A=x^{3}-27$$

Combine all terms containing A.

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

Divide both sides by x-3.

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

Dividing by x-3 undoes the multiplication by x-3.

$$A=\frac{x^{3}-27}{x-3}$$

Divide x^{3}-27 by x-3.

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

Solve for A

$$\left\{\begin{matrix}\\A=x^{2}+3x+9\text{, }&\text{unconditionally}\\A\in \mathrm{R}\text{, }&x=3\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x^{3}-27=xA-3A$$

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

$$xA-3A=x^{3}-27$$

Combine all terms containing A.

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

Divide both sides by x-3.

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

Dividing by x-3 undoes the multiplication by x-3.

$$A=\frac{x^{3}-27}{x-3}$$

Divide x^{3}-27 by x-3.

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

Solve for x (complex solution)

$$x=\frac{-\sqrt{4A-27}-3}{2}$$

$$x=3$$

$$x=\frac{\sqrt{4A-27}-3}{2}$$

Solve for x

$$\left\{\begin{matrix}\\x=3\text{, }&\text{unconditionally}\\x=\frac{\sqrt{4A-27}-3}{2}\text{; }x=\frac{-\sqrt{4A-27}-3}{2}\text{, }&A\geq \frac{27}{4}\end{matrix}\right.$$