# How do you factor completely 6a^2-15a-8a+20?

Nov 12, 2015

$\left(3 a - 4\right) \left(2 a - 5\right) = 0$.
$a = \frac{4}{3}$.
$a = \frac{5}{2}$.

#### Explanation:

We start with $6 {a}^{2} - 15 a - 8 a + 20$.
First of all, we see we can do $15 - 8 a$ easily, so
$- 15 - 8 a$ turns into $- 23 a$. So,
we have $6 {a}^{2} - 23 a + 20$.

Now, we multiply the factor of $6 {a}^{2}$, ($6$) by the last number ($20$). We get $120$. We now look for factors that add up to $23$.
For example, $- 8$ and $- 15$ add up to $23$, and multiplied, give $120$.

We now put out the equation as:
$\frac{\left(6 a - 8\right) \left(6 a - 15\right)}{6}$. We now divide the right bracket and the denominator by 3, to simplify it. We get:
$\frac{\left(6 a - 8\right) \left(2 a - 5\right)}{2}$. We now divide the left bracket and the denominator by 2, leaving the denominator as 1. We get:
$\left(3 a - 4\right) \left(2 a - 5\right)$.

Hope it Helps! :D .