Solve x^2yz-5x^2z+2yz-10z=0

$$x ^ { 2 } y z - 5 x ^ { 2 } z + 2 y z - 10 z = 0$$

Solve for y

$$\left\{\begin{matrix}\\y=5\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 10z to both sides. Anything plus zero gives itself.

$$x^{2}yz-5x^{2}z+2yz=10z$$

Add 5x^{2}z to both sides.

$$x^{2}yz+2yz=10z+5x^{2}z$$

Combine all terms containing y.

$$\left(x^{2}z+2z\right)y=10z+5x^{2}z$$

The equation is in standard form.

$$\left(zx^{2}+2z\right)y=5zx^{2}+10z$$

Divide both sides by x^{2}z+2z.

$$\frac{\left(zx^{2}+2z\right)y}{zx^{2}+2z}=\frac{5z\left(x^{2}+2\right)}{zx^{2}+2z}$$

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

$$y=\frac{5z\left(x^{2}+2\right)}{zx^{2}+2z}$$

Divide 5z\left(2+x^{2}\right) by x^{2}z+2z.

$$y=5$$

Solve for x

$$x\in \mathrm{R}$$

$$z=0\text{ or }y=5$$