How to solve this exponential equation

3^(2t+1) + 3^(t+2) = 3 1/3

put y = 3^(t+2)

=> y² = 3^(2(t+2)) = 3^(2t+4)

=> 3^(2t+1) = y²/3³ = y²/27

y² / 27 + y - 3 1/3 = 0

y² + 27 y - 90 = 0

discr = 27² + 4*90 = 33²

y = (-27 +- 33)/2 = -30 or 3

=> 3^(t+2) = 3 (-30 is impossible as 3^x > 0)

=> t+2 = 1

=> t = -1

logarithms.