Solve for P (complex solution)
\left\{\begin{matrix}P=-\frac{3x+m}{x^{2}}\text{, }&x\neq 0\\P\in \mathrm{C}\text{, }&x=0\text{ and }m=0\end{matrix}\right.
Solve for P
\left\{\begin{matrix}P=-\frac{3x+m}{x^{2}}\text{, }&x\neq 0\\P\in \mathrm{R}\text{, }&x=0\text{ and }m=0\end{matrix}\right.
Solve for m
m=-x\left(Px+3\right)
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Px^{2}+m=-3x
Subtract 3x from both sides. Anything subtracted from zero gives its negation.
Px^{2}=-3x-m
Subtract m from both sides.
x^{2}P=-3x-m
The equation is in standard form.
\frac{x^{2}P}{x^{2}}=\frac{-3x-m}{x^{2}}
Divide both sides by x^{2}.
P=\frac{-3x-m}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
P=-\frac{3x+m}{x^{2}}
Divide -3x-m by x^{2}.
Px^{2}+m=-3x
Subtract 3x from both sides. Anything subtracted from zero gives its negation.
Px^{2}=-3x-m
Subtract m from both sides.
x^{2}P=-3x-m
The equation is in standard form.
\frac{x^{2}P}{x^{2}}=\frac{-3x-m}{x^{2}}
Divide both sides by x^{2}.
P=\frac{-3x-m}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
P=-\frac{3x+m}{x^{2}}
Divide -3x-m by x^{2}.
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