Solve my^2-xy+m+6=0

$$m y ^ { 2 } - x y + m + 6 = 0$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{6-xy}{y^{2}+1}\text{, }&y\neq -i\text{ and }y\neq i\\m\in \mathrm{C}\text{, }&\left(x=-6i\text{ and }y=i\right)\text{ or }\left(x=6i\text{ and }y=-i\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Add xy to both sides. Anything plus zero gives itself.

$$my^{2}+m+6=xy$$

Subtract 6 from both sides.

$$my^{2}+m=xy-6$$

Combine all terms containing m.

$$\left(y^{2}+1\right)m=xy-6$$

Divide both sides by y^{2}+1.

$$\frac{\left(y^{2}+1\right)m}{y^{2}+1}=\frac{xy-6}{y^{2}+1}$$

Dividing by y^{2}+1 undoes the multiplication by y^{2}+1.

$$m=\frac{xy-6}{y^{2}+1}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{my^{2}+m+6}{y}\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&m=-6\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract my^{2} from both sides. Anything subtracted from zero gives its negation.

$$-xy+m+6=-my^{2}$$

Subtract m from both sides.

$$-xy+6=-my^{2}-m$$

Subtract 6 from both sides.

$$-xy=-my^{2}-m-6$$

The equation is in standard form.

$$\left(-y\right)x=-my^{2}-m-6$$

Divide both sides by -y.

$$\frac{\left(-y\right)x}{-y}=\frac{-my^{2}-m-6}{-y}$$

Dividing by -y undoes the multiplication by -y.

$$x=\frac{-my^{2}-m-6}{-y}$$

Divide -my^{2}-m-6 by -y.

$$x=my+\frac{m+6}{y}$$

Solve for m

$$m=-\frac{6-xy}{y^{2}+1}$$

Steps for Solving Linear Equation

Add xy to both sides. Anything plus zero gives itself.

$$my^{2}+m+6=xy$$

Subtract 6 from both sides.

$$my^{2}+m=xy-6$$

Combine all terms containing m.

$$\left(y^{2}+1\right)m=xy-6$$

Divide both sides by y^{2}+1.

$$\frac{\left(y^{2}+1\right)m}{y^{2}+1}=\frac{xy-6}{y^{2}+1}$$

Dividing by y^{2}+1 undoes the multiplication by y^{2}+1.

$$m=\frac{xy-6}{y^{2}+1}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{my^{2}+m+6}{y}\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&m=-6\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract my^{2} from both sides. Anything subtracted from zero gives its negation.

$$-xy+m+6=-my^{2}$$

Subtract m from both sides.

$$-xy+6=-my^{2}-m$$

Subtract 6 from both sides.

$$-xy=-my^{2}-m-6$$

The equation is in standard form.

$$\left(-y\right)x=-my^{2}-m-6$$

Divide both sides by -y.

$$\frac{\left(-y\right)x}{-y}=\frac{-my^{2}-m-6}{-y}$$

Dividing by -y undoes the multiplication by -y.

$$x=\frac{-my^{2}-m-6}{-y}$$

Divide -my^{2}-m-6 by -y.

$$x=my+\frac{m+6}{y}$$