values at which sinhx is zero

Here's the graph of the hyperbolic sine.........see for yourself where it = 0   ......

https://www.desmos.com/calculator/7scsgh5zne

$$\\sinh(x)=0\\\\ \frac{e^x-e^{-x)}}{2}=0\\\\\ e^x-e^{-x}=0\\ e^x=\frac{1}{e^x}\\ e^{2x}=1\\ 2x=0\\ x=0$$