please can you show me how to factorise this?

-12x^2 - 29x -17 = 0

First, we multiply both sides by -1 to obtain

12x^2 + 29x +17 = 0

Then, we can factor this out by getting the factors of (12)(17) which has a sum of 29:

12x^2 + 29x +17 = 0
(12x + 17)(x + 1) = 0

Solving each for x:
12x + 17 = 0
x = -17/12

x + 1 = 0
x = -1

Well, you already got your factors. And your solution set.

- 12x² - 29x - 17 = 0
12x² + 29x = - 17
x² + 29/12x = - 17/12
x² + 29/24x = - 17/24 + (29/24)²
x² + 29/24x = - 816/576 + 841/576
(x + 29/24)² = 25/576
x + 29/24 = 5/24

1st factor:
= x + 29/24 + 5/24
= x + 17/12
= 12x + 17

2nd factor:
= (12x² + 29x = - 17)/(12x + 17)
= x + 1

Answer: (12x + 17)(x + 1) are the factors.

-12x^2 - 29x - 17 = 0
-12x^2 - 12x - 17x - 17 = 0
(-12x^2 - 12x) + (-17x - 17) = 0
-12x(x + 1) - 17(x + 1) = 0
(x + 1)(-12x - 17) = 0

x + 1 = 0
x = -1

-12x - 17 = 0
-12x = 17
x = 17/-12
x = -17/12

∴ x = -17/12 , -1

12x² + 29x + 17 = 0
(12x + 17)(x + 1) = 0
x = - 17/12 , x = - 1

- ( 12 x^2+12x +17 x + 17 )

- ( 12x(x+1) + 17(x+1)
- { (12x+17)( x+1) }

-12x^2 - 29x - 17 = 0

is the same as

12x^2 + 29x + 17 = 0

(12x + 17) ( x + 1) = 0

12x + 17 = 0

12x = -17

x = -17/12

x + 1 = 0

x = -1

x = -17/12 and -1

If you want the original equation

-12x^2 - 29x - 17 = 0

(-12x - 17) ( x +1) = 0

-12x - 17 = 0

-12x = 17
x = -17/12

x + 1 = 0

x = -1

x = -17/12 and - 1