Question

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

Answer 1

`(4x +3)(x-4)`

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" "3 rArr 1 xx 3 = 3`
`1" 4" rArr 4xx4 = 16" "16-3 =13`

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

`(4x +3)(x-4)`, so the