Question

x squared minus 18x minus 144 equals 0. Solve by factoring.

Answer 1

x^2 - 18x - 144 = 0

Factorise:

We choose 2 numbers that add to -18, and multiply to 144, these numbers are +6 and -24, we put it into the brackets:

(x + 6)(x - 24)   <- x = the interted sign of the numbers inside the brackets

E.g. +6 turns into -6 and -24 turns into +24

x must = -6 or = +24

Answer 2

Answer got deleted because I have to explain it better, which I will kindly do.
(x^2 - 18x - 144) = 0
What two factors add up to equal -18 AND multiply to equal -144?
For a product to be a negative, one of the factors have to be a positive, and the other has to be a negative (positive times a negative equals a negative). 
And now that we know that, we know that the negative number has to be larger than the positive because of the -18. 
What two factors add up to equal -18 AND multiply to equal -144?
Negative 24 and positive 6.
(x - 24)(x + 6)