Noticing that -5 times -1 = 5 and -5 + -1 = -6
Hence we get (x -5) (x - 1) = 0

As 0 times anything is 0, if x = 5 we get 0 times (x - 1) = 0
and if x = 1 we get (x - 5) times 0 which also = 0.

Therefore the solutions are:  x = 5 or x = 1

(x + 1) (x + 3) = 0

Hence x = -1 or x = -3

(x + 6) (x - 4) = 0

Hence x = -6 or x = 4

(x - 3) (x - 4) = 0

Hence x = 3 or x = 4

Rearrange this into the convertional format first to make things easier:
-x² -3x + 10 = 0

Factorising we get: (-x + 2) (x + 5) = 0

Note that when x = 2, (-x + 2) becomes 0.

Hence x = 2 or x = -5

(x + 8) (x - 3) = 0

Hence x = -8 or x = 3

(2x - 5) (x + 1) = 0

Note that when x = 5/2, (2x - 5) = 0
This is because we get (2 times 5/2 - 5) = (10/2 - 5) = (5 -5)

Hence x = 5/2 or x = -1

Here we need to rearrange the equation first into the form
ax² + bx + c = 0

Subtract 2 and 3x from both sides to give:
x² - 8x + 16 = 0

(x - 4) (x - 4) = 0

Hence x = 4