How to simplify? Sin and cos

Show that  6 sin²(x) * cosx - 3cosx = -3 cos (x) cos (2x)

Now cos(2x) = 1 - 2sin²(x) so the RHS of the above becomes:

-3 cos (x) cos (2x) → -3 cos (x) (1 - 2sin²(x)) → -3 cos (x) + 6cos(x)*sin²(x) which equals the LHS of the original.

6 sin^2(x) * cosx - 3cosx  =  -3 cos (x) cos (2x)    

We can work on both sides  and show that they are equal.....

First, factor out cos x  on both sides  and write cos 2x as 1 - 2sin^2 x 

cos x [ 6sin^2 x  - 3 ]  =  cos x [ -3 (1 - 2sin^2 x) ]

Simplify

cos x [ 6sin^2 x - 3 ] = cos x [ 6sin^2 x  - 3 ]