Solve for x
x=\frac{y+1}{3y^{2}}
y\neq 0
Solve for y (complex solution)
\left\{\begin{matrix}y=\frac{\sqrt{12x+1}+1}{6x}\text{; }y=\frac{-\sqrt{12x+1}+1}{6x}\text{, }&x\neq 0\\y=-1\text{, }&x=0\end{matrix}\right.
Solve for y
\left\{\begin{matrix}y=\frac{\sqrt{12x+1}+1}{6x}\text{; }y=\frac{-\sqrt{12x+1}+1}{6x}\text{, }&x\neq 0\text{ and }x\geq -\frac{1}{12}\\y=-1\text{, }&x=0\end{matrix}\right.
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3xy^{2}=1+y
Add y to both sides.
3y^{2}x=y+1
The equation is in standard form.
\frac{3y^{2}x}{3y^{2}}=\frac{y+1}{3y^{2}}
Divide both sides by 3y^{2}.
x=\frac{y+1}{3y^{2}}
Dividing by 3y^{2} undoes the multiplication by 3y^{2}.
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