# How do you solve 4x^2=13x+12?

Jun 24, 2016

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

#### Explanation:

Find the factors of 4 and 12 which subtract to give 13.

However, 13 is an odd number which can only happen from the difference between an odd and an even number. This is a clue that the factors of 4 are not 2 and 2, because any product of these even numbers will give even numbers.
Similarly the factors of 12 are not 2 and 6, because they are both even. We find the following cross products and subtract them:

$4 \text{ } 3 \Rightarrow 1 \times 3 = 3$
$1 \text{ 4" rArr 4xx4 = 16" } 16 - 3 = 13$

However, we need -13, so the combination must be -16 and +3.

$\left(4 x + 3\right) \left(x - 4\right)$, so the