Solve x=y*(4*a)^2

$$x = y \times ( 4 \cdot a ) ^ { 2 }$$

Solve for x

$$x=16ya^{2}$$

Solution Steps

Expand \left(4a\right)^{2}.

$$x=y\times 4^{2}a^{2}$$

Calculate 4 to the power of 2 and get 16.

$$x=y\times 16a^{2}$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{y^{-\frac{1}{2}}\sqrt{x}}{4}\text{; }a=\frac{y^{-\frac{1}{2}}\sqrt{x}}{4}\text{, }&y\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}a=\frac{\sqrt{\frac{x}{y}}}{4}\text{; }a=-\frac{\sqrt{\frac{x}{y}}}{4}\text{, }&\left(x\geq 0\text{ and }y>0\right)\text{ or }\left(x\leq 0\text{ and }y<0\right)\\a\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$