Problem with Curl of Curl

I have been studying vector calculus, and came across what was to me an odd identity:

$\displaystyle \nabla\times\nabla\times\vec{F}=\nabla(\nabla\bull et\vec{F})-\nabla^2\vec{F}$

I noticed that the two terms on the right hand side are of different character.

The first term $\displaystyle \nabla(\nabla\bullet\vec{F})$, is the gradient of the divergence of the field, which is a *vector* quantity.

The second term however, $\displaystyle \nabla^2\vec{F}$ is a *scalar* quantity.

So how are we supposed to do addition between a vector and a scalar?

Something like a complex number?

Any help with understanding this would be great.

Thank you.