Solve nP_{5}=20*nP_{3}

$$n P _ { 5 } = 20 \times n P _ { 3 }$$

Solve for P_3

$$\left\{\begin{matrix}\\P_{3}=\frac{P_{5}}{20}\text{, }&\text{unconditionally}\\P_{3}\in \mathrm{R}\text{, }&n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$20nP_{3}=nP_{5}$$

The equation is in standard form.

$$20nP_{3}=P_{5}n$$

Divide both sides by 20n.

$$\frac{20nP_{3}}{20n}=\frac{P_{5}n}{20n}$$

Dividing by 20n undoes the multiplication by 20n.

$$P_{3}=\frac{P_{5}n}{20n}$$

Divide nP_{5} by 20n.

$$P_{3}=\frac{P_{5}}{20}$$

Solve for P_5

$$\left\{\begin{matrix}\\P_{5}=20P_{3}\text{, }&\text{unconditionally}\\P_{5}\in \mathrm{R}\text{, }&n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$nP_{5}=20P_{3}n$$

Divide both sides by n.

$$\frac{nP_{5}}{n}=\frac{20P_{3}n}{n}$$

Dividing by n undoes the multiplication by n.

$$P_{5}=\frac{20P_{3}n}{n}$$

Divide 20nP_{3} by n.

$$P_{5}=20P_{3}$$