Solve x^2-3yx+6z=0

$${ x }^{ 2 } -3yx+6z=0$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{x}{3}+\frac{2z}{x}\text{, }&x\neq 0\\y\in \mathrm{C}\text{, }&z=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-3yx+6z=-x^{2}$$

Subtract 6z from both sides.

$$-3yx=-x^{2}-6z$$

The equation is in standard form.

$$\left(-3x\right)y=-x^{2}-6z$$

Divide both sides by -3x.

$$\frac{\left(-3x\right)y}{-3x}=\frac{-x^{2}-6z}{-3x}$$

Dividing by -3x undoes the multiplication by -3x.

$$y=\frac{-x^{2}-6z}{-3x}$$

Divide -x^{2}-6z by -3x.

$$y=\frac{x}{3}+\frac{2z}{x}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{x}{3}+\frac{2z}{x}\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&z=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-3yx+6z=-x^{2}$$

Subtract 6z from both sides.

$$-3yx=-x^{2}-6z$$

The equation is in standard form.

$$\left(-3x\right)y=-x^{2}-6z$$

Divide both sides by -3x.

$$\frac{\left(-3x\right)y}{-3x}=\frac{-x^{2}-6z}{-3x}$$

Dividing by -3x undoes the multiplication by -3x.

$$y=\frac{-x^{2}-6z}{-3x}$$

Divide -x^{2}-6z by -3x.

$$y=\frac{x}{3}+\frac{2z}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{9y^{2}-24z}+3y}{2}$$

$$x=\frac{-\sqrt{9y^{2}-24z}+3y}{2}$$

Solve for x

$$x=\frac{\sqrt{9y^{2}-24z}+3y}{2}$$

$$x=\frac{-\sqrt{9y^{2}-24z}+3y}{2}\text{, }z\leq \frac{3y^{2}}{8}$$