# How do you solve r^2=14r?

Sep 29, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{14 r}$ from each side of the equation to equate to $0$ while keeping the equation balanced:

${r}^{2} - \textcolor{red}{14 r} = 14 r - \textcolor{red}{14 r}$

${r}^{2} - 14 r = 0$

Next, factor an $r$ out from each term on the left side of the equation:

$\left(r \cdot r\right) - \left(14 \cdot r\right) = 0$

$r \left(r - 14\right) = 0$

Now, solve each term on the left side of the equation for $0$ to find the solutions:

Solution 1:

$r = 0$

Solution 2:

$r - 14 = 0$

$r - 14 + \textcolor{red}{14} = 0 + \textcolor{red}{14}$

$r - 0 = 14$

$r = 14$

The Solutions Are: $r = 0$ and $r = 14$