How do you factor out the common factor of 
(x-1)² + 6(x-1)?

(x-1)² + 6(x-1)

Let A = (x-1)

Substitute A for (x-1)

A² + 6A

Factor out A

A(A + 6)

Change the parentheses to brackets

A[A + 6]

Now substitute (x-1) for A

(x-1)[(x-1) + 6]

Remove the parentheses inside the bracket

(x-1)[x-1 + 6]

Simplify what's inside the right brackets 

(x-1)[x+5]

Change the bracket to parentheses

(x-1)(x+5)

Edwin