# How do you solve n^2 - 7n = 0 by factoring?

Apr 13, 2018

$n = 0 \mathmr{and} n = 7$

#### Explanation:

${n}^{2} - 7 n = 0$

$n \left(n - 7\right) = 0$

To equal zero, either $n$ or $\left(n - 7\right)$ must be equal to zero

If $n = 0$:
$\textcolor{red}{n = 0}$

If $\left(n - 7\right) = 0$
$\textcolor{red}{n = 7}$

Apr 13, 2018

$n = 0 \text{ or } n = 7$

#### Explanation:

$\text{take out a "color(blue)"common factor } n$

$\Rightarrow n \left(n - 7\right) = 0$

$\text{equate each factor to zero and solve for n}$

$\Rightarrow n = 0$

$n - 7 = 0 \Rightarrow n = 7$

Apr 13, 2018

$n = 0$, $n = 7$

#### Explanation:

Factorising:

${n}^{2} - 7 n \to n \left(n - 7\right)$

Set each bracket/term equal to $0$:

$n = 0$

$n - 7 = 0$

$\to n = 7$