Question

How to solve the equation (x+k) = (x+k-1)(x+k)?

Answer 1

This solution might become quite complex.
Please try to keep up with me, and I'll go slowly:

You said                               (x + k)   =  (x + k - 1)  (x + k)

Divide each side by (x+k):      1       =  (x + k - 1)       

Add  1  to each side:               2       =  (x + k    )

Subtract 'k' from each side:    2 - k  =  x

Answer 2

(x+k) = (x+k-1)(x+k) //// (simplify with (x+k))=> 1=x+k-1 => x+k=2