# How do you solve n^2-9n=-18?

May 8, 2017

$n = - 3$ or $n = 6$

#### Explanation:

Move -18 to the other side of the 'equals to' sign
${n}^{2} - 9 n + 18 = 0$

Find two numbers which when added/subtracted will give the coefficient of n and when multiplied will give the constant number (which has no variables beside it )
${n}^{2} - 6 n - 3 n + 18 = 0$

Then factorise common variables/constants
$n \left(n - 6\right) + 3 \left(n - 6\right) = 0$
$\left(n + 3\right) \left(n - 6\right) = 0$

$\left(n + 3\right) = 0$ or $\left(n - 6\right) = 0$
So $n = - 3$ or $n = 6$