Solve left(4xright)^2*5y=z

$${ \left(4x \right) }^{ 2 } \times 5y=z$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{z}{80x^{2}}\text{, }&x\neq 0\\y\in \mathrm{C}\text{, }&z=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$4^{2}x^{2}\times 5y=z$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}\times 5y=z$$

Multiply 16 and 5 to get 80.

$$80x^{2}y=z$$

Divide both sides by 80x^{2}.

$$\frac{80x^{2}y}{80x^{2}}=\frac{z}{80x^{2}}$$

Dividing by 80x^{2} undoes the multiplication by 80x^{2}.

$$y=\frac{z}{80x^{2}}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{z}{80x^{2}}\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&z=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$4^{2}x^{2}\times 5y=z$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}\times 5y=z$$

Multiply 16 and 5 to get 80.

$$80x^{2}y=z$$

Divide both sides by 80x^{2}.

$$\frac{80x^{2}y}{80x^{2}}=\frac{z}{80x^{2}}$$

Dividing by 80x^{2} undoes the multiplication by 80x^{2}.

$$y=\frac{z}{80x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{y^{-\frac{1}{2}}\sqrt{5z}}{20}\text{; }x=\frac{y^{-\frac{1}{2}}\sqrt{5z}}{20}\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&z=0\text{ and }y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{\frac{5z}{y}}}{20}\text{; }x=-\frac{\sqrt{\frac{5z}{y}}}{20}\text{, }&\left(z\geq 0\text{ and }y>0\right)\text{ or }\left(z\leq 0\text{ and }y<0\right)\\x\in \mathrm{R}\text{, }&z=0\text{ and }y=0\end{matrix}\right.$$