Solve (x^2b^2-7xb+12)y=x^2

$$( x ^ { 2 } b ^ { 2 } - 7 x b + 12 ) y = x ^ { 2 }$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{\sqrt{y\left(4x^{2}+y\right)}-7y}{2xy}\text{; }b=\frac{\sqrt{y\left(4x^{2}+y\right)}+7y}{2xy}\text{, }&x\neq 0\text{ and }y\neq 0\\b\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{y\left(yb^{2}+48\right)}+7by}{2\left(yb^{2}-1\right)}\text{; }x=\frac{-\sqrt{y\left(yb^{2}+48\right)}+7by}{2\left(yb^{2}-1\right)}\text{, }&y=0\text{ or }\left(b\neq -y^{-\frac{1}{2}}\text{ and }b\neq y^{-\frac{1}{2}}\right)\\x=\frac{12}{7b}\text{, }&y=\frac{1}{b^{2}}\text{ and }b\neq 0\end{matrix}\right.$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{\sqrt{4x^{2}+y}-7\sqrt{y}}{2\sqrt{y}x}\text{; }b=\frac{\sqrt{4x^{2}+y}+7\sqrt{y}}{2\sqrt{y}x}\text{, }&x\neq 0\text{ and }y>0\\b=-\frac{\sqrt{y\left(4x^{2}+y\right)}-7y}{2xy}\text{; }b=\frac{\sqrt{y\left(4x^{2}+y\right)}+7y}{2xy}\text{, }&x\neq 0\text{ and }y\leq -4x^{2}\text{ and }|x|\leq \frac{\sqrt{-y}}{2}\text{ and }y<0\\b\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{y\left(yb^{2}+48\right)}+7by}{2\left(yb^{2}-1\right)}\text{; }x=\frac{-\sqrt{y\left(yb^{2}+48\right)}+7by}{2\left(yb^{2}-1\right)}\text{, }&\left(b\geq 4\sqrt{-\frac{3}{y}}\text{ and }y\leq 0\right)\text{ or }\left(y>0\text{ and }b\neq -\frac{1}{\sqrt{y}}\right)\text{ or }\left(b\neq -\frac{1}{\sqrt{y}}\text{ and }b\leq -4\sqrt{-\frac{3}{y}}\right)\text{ or }y=0\text{ or }\left(b\neq \frac{1}{\sqrt{y}}\text{ and }b\geq 4\sqrt{-\frac{3}{y}}\right)\text{ or }\left(b\neq \frac{1}{\sqrt{y}}\text{ and }y\geq 0\right)\\x=\frac{12}{7b}\text{, }&y=\frac{1}{b^{2}}\text{ and }b\neq 0\end{matrix}\right.$$