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