Solve xθ^2+yθ+z=0

$$x { \theta }^{ 2 } +y \theta +z=0$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Subtract y\theta from both sides. Anything subtracted from zero gives its negation.

$$x\theta ^{2}+z=-y\theta$$

Subtract z from both sides.

$$x\theta ^{2}=-y\theta -z$$

The equation is in standard form.

$$\theta ^{2}x=-y\theta -z$$

Divide both sides by \theta ^{2}.

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

Dividing by \theta ^{2} undoes the multiplication by \theta ^{2}.

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

Divide -y\theta -z by \theta ^{2}.

$$x=-\frac{y\theta +z}{\theta ^{2}}$$

Solve for y (complex solution)

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

Steps for Solving Linear Equation

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

$$y\theta +z=-x\theta ^{2}$$

Subtract z from both sides.

$$y\theta =-x\theta ^{2}-z$$

The equation is in standard form.

$$\theta y=-x\theta ^{2}-z$$

Divide both sides by \theta .

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

Dividing by \theta undoes the multiplication by \theta .

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

Divide -x\theta ^{2}-z by \theta .

$$y=-x\theta -\frac{z}{\theta }$$

Solve for x

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

Steps for Solving Linear Equation

Subtract y\theta from both sides. Anything subtracted from zero gives its negation.

$$x\theta ^{2}+z=-y\theta$$

Subtract z from both sides.

$$x\theta ^{2}=-y\theta -z$$

The equation is in standard form.

$$\theta ^{2}x=-y\theta -z$$

Divide both sides by \theta ^{2}.

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

Dividing by \theta ^{2} undoes the multiplication by \theta ^{2}.

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

Divide -y\theta -z by \theta ^{2}.

$$x=-\frac{y\theta +z}{\theta ^{2}}$$

Solve for y

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

Steps for Solving Linear Equation

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

$$y\theta +z=-x\theta ^{2}$$

Subtract z from both sides.

$$y\theta =-x\theta ^{2}-z$$

The equation is in standard form.

$$\theta y=-x\theta ^{2}-z$$

Divide both sides by \theta .

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

Dividing by \theta undoes the multiplication by \theta .

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

Divide -x\theta ^{2}-z by \theta .

$$y=-x\theta -\frac{z}{\theta }$$