# How do you solve 15x^2 + 26x + 8 = 0?

Jan 4, 2016

Find a suitable split of the middle term, then factor by grouping to find:

$15 {x}^{2} + 26 x + 8 = \left(5 x + 2\right) \left(3 x + 4\right)$

#### Explanation:

Find two factors of $A C = 15 \cdot 8 = 120$ whose sum is $B = 26$.

The pair $20$, $6$ works:

$20 \times 6 = 120$

$20 + 6 = 26$

Then use these to split the middle term and factor by grouping:

$15 {x}^{2} + 26 x + 8$

$= \left(15 {x}^{2} + 20 x\right) + \left(6 x + 8\right)$

$= 5 x \left(3 x + 4\right) + 2 \left(3 x + 4\right)$

$= \left(5 x + 2\right) \left(3 x + 4\right)$