How do you get (x'^T)R = (x-t)^T from the first equation?
Recall that a rotation matrix $R$ is unitary, which means that its inverse is $R^T$. Thus, $x' = R(x-t) \rightarrow R^T x' = x-t \rightarrow x'^T R = (x-t)^T$.
How do you get (x'^T)R = (x-t)^T from the first equation?
Recall that a rotation matrix $R$ is unitary, which means that its inverse is $R^T$. Thus, $x' = R(x-t) \rightarrow R^T x' = x-t \rightarrow x'^T R = (x-t)^T$.