How would I do this?

(cos x + 1)(√2 cos x - 1) = 0      set each factor to 0

cos x + 1 = 0       add 1 to  both sides

cos x  = -1

And this happens at  pi  on  [0, 2pi]  

And

√2 cos x - 1  = 0      add 1 to both sides

√2 cos x  = 1          divide both sides by √2

cos x =    1 / √2

And this happens at   pi/4    and 7pi/4    on [0, 2pi]