Solve 20x_1^2+40x_{1}x_{2}=0

$$20 x _ { 1 } ^ { 2 } + 40 x _ { 1 } x _ { 2 } = 0$$

Solve for x_2

$$\left\{\begin{matrix}\\x_{2}=-\frac{x_{1}}{2}\text{, }&\text{unconditionally}\\x_{2}\in \mathrm{R}\text{, }&x_{1}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 20x_{1}^{2} from both sides. Anything subtracted from zero gives its negation.

$$40x_{1}x_{2}=-20x_{1}^{2}$$

Divide both sides by 40x_{1}.

$$\frac{40x_{1}x_{2}}{40x_{1}}=-\frac{20x_{1}^{2}}{40x_{1}}$$

Dividing by 40x_{1} undoes the multiplication by 40x_{1}.

$$x_{2}=-\frac{20x_{1}^{2}}{40x_{1}}$$

Divide -20x_{1}^{2} by 40x_{1}.

$$x_{2}=-\frac{x_{1}}{2}$$

Solve for x_1

$$x_{1}=-2x_{2}$$

$$x_{1}=0$$