How to factorize this in steps? (I don't want to solve for z I want the factorization steps)

1 - 0.1/z^2 - 0.15/z

This cannot be reduced any further !!.

1 - 0.15z^-1 - 0.1z^-2

 

To get rid of the denominators, I am going to multiply the expression by the fraction  (100z²)/(100z²).

This gives  100z²(1 - 0.15z^-1 - 0.1z^-2) / (100z²).

Multiplying out:  (100z² + 15z- 10) / (100z²).

Now, I'm going to factor out a 5 from the numerator:  5(20z² + 3z - 2) / (100z²).

Cancelling the 5 from both the numerator and denominator:  (20z² + 3z - 2) / (20z²).

20z² + 3z - 2 can be factored into (5z - 2)(4z + 1).

So, an answer is:  (5z - 2)(4z + 1) / (20z²).

If you were to solve as a quadratic,---

multiply through by (z^2)      ( both sides of course,but I'm assuming you're solving for right hand side = 0)       left hand side becomes

(z^2) - 0.15 z - 0.1               now multiply both sides by  100, left hand side becomes

100z^2 - 15z -10     which you can now factorise   as

(20z +5)(5z -2)   and solve accordingly.

You have asked this question at least twice and it has been answered at least twice!

Do not waste answerers time like this again!