Answer
Yes
Work Step by Step
We need to rearrange the equation as: $t^2-4t+3=0$
$t^2--3t-t+3=0$
or, $ t= 3$
Now, we need to rearrange the equation as: $t^2-7t+12=0$
$t^2-6t-t+12=0$
This gives: $ t= 3$
Further, set the $z$ component of the two equations equal to each other first.
We have $t^2=5t-6$
or, $t^2-5t+6=0 \implies t^2-6t+t+6=0$
This gives $t=3$
Hence, all three equations gives the same result.
So, the answer is Yes.