Solve 2left(x^2right)^2=(yz)z/2

$$2 { \left( { x }^{ 2 } \right) }^{ 2 } =(yz) \frac{ z }{ 2 }$$

Solve for y (complex solution)

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$4\left(x^{2}\right)^{2}=yzz$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$4x^{4}=yzz$$

Multiply z and z to get z^{2}.

$$4x^{4}=yz^{2}$$

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

$$yz^{2}=4x^{4}$$

The equation is in standard form.

$$z^{2}y=4x^{4}$$

Divide both sides by z^{2}.

$$\frac{z^{2}y}{z^{2}}=\frac{4x^{4}}{z^{2}}$$

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

$$y=\frac{4x^{4}}{z^{2}}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{4x^{4}}{z^{2}}\text{, }&z\neq 0\\y\in \mathrm{R}\text{, }&x=0\text{ and }z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$4\left(x^{2}\right)^{2}=yzz$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$4x^{4}=yzz$$

Multiply z and z to get z^{2}.

$$4x^{4}=yz^{2}$$

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

$$yz^{2}=4x^{4}$$

The equation is in standard form.

$$z^{2}y=4x^{4}$$

Divide both sides by z^{2}.

$$\frac{z^{2}y}{z^{2}}=\frac{4x^{4}}{z^{2}}$$

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

$$y=\frac{4x^{4}}{z^{2}}$$

Solve for x (complex solution)

$$x=\frac{i\sqrt[4]{y}\sqrt{2z}}{2}$$

$$x=\frac{\sqrt[4]{y}\sqrt{2z}}{2}$$

$$x=-\frac{\sqrt[4]{y}\sqrt{2z}}{2}$$

$$x=-\frac{i\sqrt[4]{y}\sqrt{2z}}{2}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{-2\sqrt{y}z}}{2}\text{; }x=-\frac{\sqrt{-2\sqrt{y}z}}{2}\text{, }&y=0\text{ or }\left(y\geq 0\text{ and }z\leq 0\right)\\x=\frac{\sqrt{2\sqrt{y}z}}{2}\text{; }x=-\frac{\sqrt{2\sqrt{y}z}}{2}\text{, }&y=0\text{ or }\left(z\geq 0\text{ and }y\geq 0\right)\\x=0\text{, }&z=0\end{matrix}\right.$$