Solve for N
\left\{\begin{matrix}\\N=1\text{, }&\text{unconditionally}\\N\in \mathrm{R}\text{, }&P=0\end{matrix}\right.
Solve for P
\left\{\begin{matrix}\\P=0\text{, }&\text{unconditionally}\\P\in \mathrm{R}\text{, }&N=1\end{matrix}\right.
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NP=P
Swap sides so that all variable terms are on the left hand side.
PN=P
The equation is in standard form.
\frac{PN}{P}=\frac{P}{P}
Divide both sides by P.
N=\frac{P}{P}
Dividing by P undoes the multiplication by P.
N=1
Divide P by P.
P-NP=0
Subtract NP from both sides.
\left(1-N\right)P=0
Combine all terms containing P.
P=0
Divide 0 by 1-N.
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