# How do you solve 3x^2+17x+20=0?

May 5, 2018

$x = \frac{- 5}{3}$ or $x = - 4$

#### Explanation:

$3 {x}^{2} + 17 x + 20 = 0$

Can be factored by finding the factors for $a \cdot c$

$3 \cdot 20 = 60$

The factors of 60 are
$1 \cdot 60$
$2 \cdot 30$
$3 \cdot 20$
$4 \cdot 15$
$5 \cdot 12$
$6 \cdot 10$

The factor pattern that adds up to the middle term is $5 + 12 = 17$

Set the Polynomial up as

$3 {x}^{2} + 12 x + 5 x + 20$

Now factor by grouping

$\left[3 {x}^{2} + 12 x\right] \left[+ 5 x + 20\right]$

$3 x \left(x + 4\right) + 5 \left(x + 4\right)$

So the common factor is $\left(x + 4\right)$

$\left(3 x + 5\right) \left(x + 4\right) = 0$

Set both factors equal to zero

$3 x + 5 = 0$

$x = - \frac{5}{3}$

$x + 4 = 0$

$x = - 4$