If you have more than one question, you need to make separate posts.
To factor using decomposition, you need to find the factors of the product of the first and last coefficient that add to the middle coefficient.
In this case, we are looking for factors of 6x1=6 that add to -7, which are -6 and -1.
Then split apart the middle term using these factors. Finally, factor using group factoring twice.
`6a^2-7a+1` split middle term
`=6a^2-6a-a+1` factor by grouping
`=6a(a-1)-1(a-1)` common factoring
The expression factors into `(a-1)(6a-1)` .