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It will not factor unless you set it to 0, solve for the irrational roots and then write (x-root1)(x-root2)
now you need the factors of 6. So 1x6, 2x3 and that's it.
if you look at the middle term, you see its just x, or 1x. so this means the terms you also factor, will differ by only 1. So that means the factors are 2 and 3. (with the 2x to start with, it might not differ by 1, but will if the terms are both x's, you'll figure it out the more you try)
Since 6 is negative, you know you have one negative factor and one positive. If both are positive or both negative, when multiplied together will give you a positive number.
So, you can guess and check or just figure out by inspection. After doing enough of these you'll get it fast.
The answer is (2x -3 )*(x + 2) so this would give you 2x^2 + 4x - 3x - 6 which is equal to your question.