Solve for p
\left\{\begin{matrix}p=\frac{A}{rt+1}\text{, }&t=0\text{ or }r\neq -\frac{1}{t}\\p\in \mathrm{R}\text{, }&A=0\text{ and }r=-\frac{1}{t}\text{ and }t\neq 0\end{matrix}\right.
Solve for A
A=p\left(rt+1\right)
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p+prt=A
Swap sides so that all variable terms are on the left hand side.
\left(1+rt\right)p=A
Combine all terms containing p.
\left(rt+1\right)p=A
The equation is in standard form.
\frac{\left(rt+1\right)p}{rt+1}=\frac{A}{rt+1}
Divide both sides by 1+rt.
p=\frac{A}{rt+1}
Dividing by 1+rt undoes the multiplication by 1+rt.
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