The number of solutions for the equation ${\cos }^{-1}x+{\cos }^{-1}2x+\pi =0$

The given equation is ${\cos }^{-1}x+{\cos }^{-1}2x+\pi =0$

It implies that ${\cos }^{-1}x+{\cos }^{-1}2x=-\mathrm{\pi }$

But the range of ${\cos }^{-1}x$ is $\left[0,\mathrm{\pi }\right]$, no negative value

hence the given equation has no solutions.

Therefore, the number of solutions for the equation ${\cos }^{-1}x+{\cos }^{-1}2x+\pi =0$ is $\boxed{\mathbf{0}}$