Solve aA^2=2x^2+4x^2

$$a A ^ { 2 } = 2 x ^ { 2 } + 4 x ^ { 2 }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=6\times \left(\frac{x}{A}\right)^{2}\text{, }&A\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }A=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 2x^{2} and 4x^{2} to get 6x^{2}.

$$aA^{2}=6x^{2}$$

The equation is in standard form.

$$A^{2}a=6x^{2}$$

Divide both sides by A^{2}.

$$\frac{A^{2}a}{A^{2}}=\frac{6x^{2}}{A^{2}}$$

Dividing by A^{2} undoes the multiplication by A^{2}.

$$a=\frac{6x^{2}}{A^{2}}$$

Solve for a

$$\left\{\begin{matrix}a=6\times \left(\frac{x}{A}\right)^{2}\text{, }&A\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }A=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 2x^{2} and 4x^{2} to get 6x^{2}.

$$aA^{2}=6x^{2}$$

The equation is in standard form.

$$A^{2}a=6x^{2}$$

Divide both sides by A^{2}.

$$\frac{A^{2}a}{A^{2}}=\frac{6x^{2}}{A^{2}}$$

Dividing by A^{2} undoes the multiplication by A^{2}.

$$a=\frac{6x^{2}}{A^{2}}$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=-\sqrt{6}a^{-\frac{1}{2}}x\text{; }A=\sqrt{6}a^{-\frac{1}{2}}x\text{, }&a\neq 0\\A\in \mathrm{C}\text{, }&x=0\text{ and }a=0\end{matrix}\right.$$

Solve for A

$$\left\{\begin{matrix}A=\sqrt{\frac{6}{a}}x\text{; }A=-\sqrt{\frac{6}{a}}x\text{, }&a>0\\A=0\text{, }&x=0\text{ and }a\neq 0\\A\in \mathrm{R}\text{, }&x=0\text{ and }a=0\end{matrix}\right.$$