Solve n(2xy)-(zx)(zy)quadn=6

$$n ( 2 x y ) - ( z x ) ( z y ) \quad n = 6$$

Solve for n

$$n=\frac{6}{xy\left(2-z^{2}\right)}$$

$$y\neq 0\text{ and }x\neq 0\text{ and }|z|\neq \sqrt{2}$$

Steps for Solving Linear Equation

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

$$n\times 2xy-z^{2}xyn=6$$

Reorder the terms.

$$-nxyz^{2}+2nxy=6$$

Combine all terms containing n.

$$\left(-xyz^{2}+2xy\right)n=6$$

The equation is in standard form.

$$\left(2xy-xyz^{2}\right)n=6$$

Divide both sides by -xyz^{2}+2xy.

$$\frac{\left(2xy-xyz^{2}\right)n}{2xy-xyz^{2}}=\frac{6}{2xy-xyz^{2}}$$

Dividing by -xyz^{2}+2xy undoes the multiplication by -xyz^{2}+2xy.

$$n=\frac{6}{2xy-xyz^{2}}$$

Divide 6 by -xyz^{2}+2xy.

$$n=\frac{6}{xy\left(2-z^{2}\right)}$$

Solve for x

$$x=\frac{6}{ny\left(2-z^{2}\right)}$$

$$y\neq 0\text{ and }n\neq 0\text{ and }|z|\neq \sqrt{2}$$

Steps for Solving Linear Equation

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

$$n\times 2xy-z^{2}xyn=6$$

Reorder the terms.

$$-nxyz^{2}+2nxy=6$$

Combine all terms containing x.

$$\left(-nyz^{2}+2ny\right)x=6$$

The equation is in standard form.

$$\left(2ny-nyz^{2}\right)x=6$$

Divide both sides by 2yn-ynz^{2}.

$$\frac{\left(2ny-nyz^{2}\right)x}{2ny-nyz^{2}}=\frac{6}{2ny-nyz^{2}}$$

Dividing by 2yn-ynz^{2} undoes the multiplication by 2yn-ynz^{2}.

$$x=\frac{6}{2ny-nyz^{2}}$$

Divide 6 by 2yn-ynz^{2}.

$$x=\frac{6}{ny\left(2-z^{2}\right)}$$