Solve 6x/10xy=z

$$\frac{ 6x }{ 10 } xy = z$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{5z}{3x^{2}}\text{, }&x\neq 0\\y\in \mathrm{C}\text{, }&z=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Divide 6x by 10 to get \frac{3}{5}x.

$$\frac{3}{5}xxy=z$$

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

$$\frac{3}{5}x^{2}y=z$$

The equation is in standard form.

$$\frac{3x^{2}}{5}y=z$$

Divide both sides by \frac{3}{5}x^{2}.

$$\frac{5\times \frac{3x^{2}}{5}y}{3x^{2}}=\frac{5z}{3x^{2}}$$

Dividing by \frac{3}{5}x^{2} undoes the multiplication by \frac{3}{5}x^{2}.

$$y=\frac{5z}{3x^{2}}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{5z}{3x^{2}}\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&z=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Divide 6x by 10 to get \frac{3}{5}x.

$$\frac{3}{5}xxy=z$$

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

$$\frac{3}{5}x^{2}y=z$$

The equation is in standard form.

$$\frac{3x^{2}}{5}y=z$$

Divide both sides by \frac{3}{5}x^{2}.

$$\frac{5\times \frac{3x^{2}}{5}y}{3x^{2}}=\frac{5z}{3x^{2}}$$

Dividing by \frac{3}{5}x^{2} undoes the multiplication by \frac{3}{5}x^{2}.

$$y=\frac{5z}{3x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{y^{-\frac{1}{2}}\sqrt{15z}}{3}\text{; }x=\frac{y^{-\frac{1}{2}}\sqrt{15z}}{3}\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&z=0\text{ and }y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{\frac{15z}{y}}}{3}\text{; }x=-\frac{\sqrt{\frac{15z}{y}}}{3}\text{, }&\left(z\geq 0\text{ and }y>0\right)\text{ or }\left(z\leq 0\text{ and }y<0\right)\\x\in \mathrm{R}\text{, }&z=0\text{ and }y=0\end{matrix}\right.$$