How to factorize this in steps? (I don't want to solve for z I want the factorization steps)
1- 0.15z-1 - 0.1z-2
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.