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