Solve nP_{3}=6[nC_{5}]

$$n P _ { 3 } = 6 [ n C _ { 5 } ]$$

Solve for C_5

$$\left\{\begin{matrix}\\C_{5}=\frac{P_{3}}{6}\text{, }&\text{unconditionally}\\C_{5}\in \mathrm{R}\text{, }&n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$6nC_{5}=nP_{3}$$

The equation is in standard form.

$$6nC_{5}=P_{3}n$$

Divide both sides by 6n.

$$\frac{6nC_{5}}{6n}=\frac{P_{3}n}{6n}$$

Dividing by 6n undoes the multiplication by 6n.

$$C_{5}=\frac{P_{3}n}{6n}$$

Divide nP_{3} by 6n.

$$C_{5}=\frac{P_{3}}{6}$$

Solve for P_3

$$\left\{\begin{matrix}\\P_{3}=6C_{5}\text{, }&\text{unconditionally}\\P_{3}\in \mathrm{R}\text{, }&n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$nP_{3}=6C_{5}n$$

Divide both sides by n.

$$\frac{nP_{3}}{n}=\frac{6C_{5}n}{n}$$

Dividing by n undoes the multiplication by n.

$$P_{3}=\frac{6C_{5}n}{n}$$

Divide 6nC_{5} by n.

$$P_{3}=6C_{5}$$