# How do you solve x^2 - 20x = 0 by factoring?

Mar 10, 2018

The solutions are $x = 0$ and $20$.

#### Explanation:

First, split up ${x}^{2}$ into $x \cdot x$ and $20 x$ into $x \cdot 20$.

Then, use the distributive property backward.

Lastly, set each of the factors equal to $0$ and solve for $x$ in each one:

${x}^{2} - 20 x = 0$

$\textcolor{red}{x} \cdot \textcolor{b l u e}{x} - \textcolor{red}{x} \cdot \textcolor{b l u e}{20} = 0$

$\left(\textcolor{red}{x}\right) \left(\textcolor{b l u e}{x} \textcolor{b l u e}{-} \textcolor{b l u e}{20}\right) = 0$

Setting each of the factors equal to $0$:

color(white){color(black)( (color(red)x=0, qquadqquadcolor(blue)(x-20)=0), (color(red)x=0, qquadqquadcolor(blue)(x-20)color(green)+color(green)20=0color(green)+color(green)20), (color(red)x=0, qquadqquadcolor(blue)(x)color(red)cancel(color(blue)(-)color(blue)(20)color(green)+color(green)20)=0color(green)+color(green)20), (color(red)x=0, qquadqquadcolor(blue)(x)=0+20), (color(red)x=0, qquadqquadcolor(blue)x=20):}

These are the solutions. Hope this helped!