Find the pt of inflection and local max. of surge ALGEBRAICALLY

Just started calculus, so please treat me like a moron when explaining and show all working haha :)
My surge function is y=8te^-0.45t
I found the FIRST DERIVATIVE to be: 8e^-0.45t - 3.6te^-0.45t
And the SECOND DERIVATIVE to be: -7.2e^-0.45t + 1.62te^-0.45t
I know that to find the maximum, i must somehow solve 1st deriv. = to 0.. but i don't know how
I also know that to find pt of inflection, i must solve 2nd deriv. = to 0.. i also don't know how =(

Could you please find the pt of inflection and maximum algebraically?
Thanks :)
SHOW Working and receive 5/5 star best answer! :)

HINT: the EXPONENTIAL is never ZERO....{ 8 / 3.6 ; 7.2 / 1.62 }