Solve ax^2+bx=0

$$a x ^ { 2 } + b x = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{b}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract bx from both sides. Anything subtracted from zero gives its negation.

$$ax^{2}=-bx$$

The equation is in standard form.

$$x^{2}a=-bx$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=-\frac{bx}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$a=-\frac{bx}{x^{2}}$$

Divide -bx by x^{2}.

$$a=-\frac{b}{x}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}\\b=-ax\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$bx=-ax^{2}$$

The equation is in standard form.

$$xb=-ax^{2}$$

Divide both sides by x.

$$\frac{xb}{x}=-\frac{ax^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$b=-\frac{ax^{2}}{x}$$

Divide -ax^{2} by x.

$$b=-ax$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{b}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract bx from both sides. Anything subtracted from zero gives its negation.

$$ax^{2}=-bx$$

The equation is in standard form.

$$x^{2}a=-bx$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=-\frac{bx}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$a=-\frac{bx}{x^{2}}$$

Divide -bx by x^{2}.

$$a=-\frac{b}{x}$$

Solve for b

$$\left\{\begin{matrix}\\b=-ax\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$bx=-ax^{2}$$

The equation is in standard form.

$$xb=-ax^{2}$$

Divide both sides by x.

$$\frac{xb}{x}=-\frac{ax^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$b=-\frac{ax^{2}}{x}$$

Divide -ax^{2} by x.

$$b=-ax$$