x² - 3x = 4

To solve this by factorisation
we need to have 0 on the right hand side

Subtract 4 from both sides
[or add - 4 to both sides]
x² - 3x - 4 = 4 - 4
x² - 3x - 4 = 0

Create 2 sets of brackets = 0
(          )(          ) = 0

Put x at the start of each set
(x         )(x         ) = 0

Need 2 numbers which
multiply to give -4
and add to give -3
+1 × -4 = -4
+1 + -4 = -3

Put one number into each set of brackets
(x + 1)(x - 4) = 0

We only get 0 by multiplication
if one of the things we start with is 0
(x + 1)(x - 4) = 0
so    (x + 1) = 0    =>    x = -1
or    (x - 4) = 0   =>    x = +4