Solve for A (complex solution)
\left\{\begin{matrix}A=-\frac{-x^{3}+2x-u}{3xy}\text{, }&y\neq 0\text{ and }x\neq 0\\A\in \mathrm{C}\text{, }&\left(u=0\text{ and }x=0\right)\text{ or }\left(u=x\left(2-x^{2}\right)\text{ and }y=0\right)\end{matrix}\right.
Solve for A
\left\{\begin{matrix}A=-\frac{-x^{3}+2x-u}{3xy}\text{, }&y\neq 0\text{ and }x\neq 0\\A\in \mathrm{R}\text{, }&\left(u=0\text{ and }x=0\right)\text{ or }\left(u=x\left(2-x^{2}\right)\text{ and }y=0\right)\end{matrix}\right.
Solve for u
u=-x\left(x^{2}-3Ay-2\right)
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2x-x^{3}+3xyA=u
Swap sides so that all variable terms are on the left hand side.
-x^{3}+3xyA=u-2x
Subtract 2x from both sides.
3xyA=u-2x+x^{3}
Add x^{3} to both sides.
3xyA=x^{3}-2x+u
The equation is in standard form.
\frac{3xyA}{3xy}=\frac{x^{3}-2x+u}{3xy}
Divide both sides by 3xy.
A=\frac{x^{3}-2x+u}{3xy}
Dividing by 3xy undoes the multiplication by 3xy.
2x-x^{3}+3xyA=u
Swap sides so that all variable terms are on the left hand side.
-x^{3}+3xyA=u-2x
Subtract 2x from both sides.
3xyA=u-2x+x^{3}
Add x^{3} to both sides.
3xyA=x^{3}-2x+u
The equation is in standard form.
\frac{3xyA}{3xy}=\frac{x^{3}-2x+u}{3xy}
Divide both sides by 3xy.
A=\frac{x^{3}-2x+u}{3xy}
Dividing by 3xy undoes the multiplication by 3xy.
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