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x squared - 3x - 40 = 0

.. and it gives the following as a model answer: (where I've wriiten right or wrong there is a tick or a cross)

try 2 x 20x, 4 x 10x, 5 x 8 (right)

(x-5) (x + 8) (wrong)

(x+5) (x-8) (right)

x = -5 or 8

I have no idea what this method is and why it has been used here. Can anyone please expain it to me?

Thanks