Solve P(13)*P_{B}(A)=1/(B_{M}A)

$$P ( 13 ) \times P _ { B } ( A ) = 1 / ( B _ { M } A )$$

Solve for B_M

$$B_{M}=\frac{1}{13PP_{B}A^{2}}$$

$$A\neq 0\text{ and }P_{B}\neq 0\text{ and }P\neq 0$$

Steps for Solving Linear Equation

Variable B_{M} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by AB_{M}.

$$P\times 13P_{B}AAB_{M}=1$$

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

$$P\times 13P_{B}A^{2}B_{M}=1$$

The equation is in standard form.

$$13PP_{B}A^{2}B_{M}=1$$

Divide both sides by 13PP_{B}A^{2}.

$$\frac{13PP_{B}A^{2}B_{M}}{13PP_{B}A^{2}}=\frac{1}{13PP_{B}A^{2}}$$

Dividing by 13PP_{B}A^{2} undoes the multiplication by 13PP_{B}A^{2}.

$$B_{M}=\frac{1}{13PP_{B}A^{2}}$$

Variable B_{M} cannot be equal to 0.

$$B_{M}=\frac{1}{13PP_{B}A^{2}}\text{, }B_{M}\neq 0$$

Solve for A (complex solution)

$$A=-\frac{\sqrt{13}B_{M}^{-\frac{1}{2}}P^{-\frac{1}{2}}P_{B}^{-\frac{1}{2}}}{13}$$

$$A=\frac{\sqrt{13}B_{M}^{-\frac{1}{2}}P^{-\frac{1}{2}}P_{B}^{-\frac{1}{2}}}{13}\text{, }B_{M}\neq 0\text{ and }P_{B}\neq 0\text{ and }P\neq 0$$

Solve for A

$$A=\frac{\sqrt{\frac{13}{B_{M}PP_{B}}}}{13}$$

$$A=-\frac{\sqrt{\frac{13}{B_{M}PP_{B}}}}{13}\text{, }\left(B_{M}<0\text{ and }P_{B}<0\text{ and }P>0\right)\text{ or }\left(B_{M}<0\text{ and }P<0\text{ and }P_{B}>0\right)\text{ or }\left(P>0\text{ and }P_{B}>0\text{ and }B_{M}>0\right)\text{ or }\left(P_{B}<0\text{ and }P<0\text{ and }B_{M}>0\right)$$