Solve for p
\left\{\begin{matrix}p=-\frac{6x^{2}+5x-y+1}{x^{3}}\text{, }&x\neq 0\\p\in \mathrm{R}\text{, }&y=1\text{ and }x=0\end{matrix}\right.
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px^{3}+6x^{2}+5x+1=y
Swap sides so that all variable terms are on the left hand side.
px^{3}+5x+1=y-6x^{2}
Subtract 6x^{2} from both sides.
px^{3}+1=y-6x^{2}-5x
Subtract 5x from both sides.
px^{3}=y-6x^{2}-5x-1
Subtract 1 from both sides.
x^{3}p=-6x^{2}-5x+y-1
The equation is in standard form.
\frac{x^{3}p}{x^{3}}=\frac{-6x^{2}-5x+y-1}{x^{3}}
Divide both sides by x^{3}.
p=\frac{-6x^{2}-5x+y-1}{x^{3}}
Dividing by x^{3} undoes the multiplication by x^{3}.
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