t² -7 + 12t⁻² = 0
Multiply each side by t² :
t⁴ -7t² + 12 = 0
This is a quadratic equation in the variable ' t² '.
For just a moment, to avoid confusion, let U = t².
Then the equation is
U² - 7U + 12 = 0
whence
(U - 4) (U - 3) = 0
and
U = 4 and U = 3 .
Now we can go back to ' t² ' in place of U :
t² = 4
t = +2 and t = -2
t² = 3
t = +√3 and t = -√3