Well just say you're solving an equation and you're at the RTP step.
You have to prove LHS = RHS, which is
k/6 (k+1)(2k+1) + (k+1)^2 = (k+1)/6 (k+2)(2k+3)
Can you simplify and expand left hand side, then simplify and expand the right hand side, so they're equal?
I'm not moving the equation...