Math Help - Word problems

A model rocket is launched from the roof of a building. It's flight path through the air is modeled by h=-5t²+23t+10, where h is the height of the rocket above ground in meters and t is the time after the launch in seconds.

A) when does the rocket hit the ground?

I got this far H= -1(5t²-23t-10) -23-50
H= -1(t-25)(t+2) -25+2
The teacher answer has this..........
H= -1(5t²-23t-10)
H= -(t-5)(5t+2)

t-5= 0 5t+2=0
t=5 t=-2/5

Where does 5t come from?
I don't get the whole H= -5t²+23t+10 equation what does -5 stand for? 23t? 10?
Teacher just taught me the equation and I follow it but, I kinda dont get the whole thing.

How did you get these steps?

Originally Posted by buck

I got this far H= -1(5t²-23t-10) -23-50
H= -1(t-25)(t+2) -25+2

All you need to do is solve where

i.e.

You can factor the RHS and apply the null factor law like in your teachers solution or just use the quadratic formula.

Which method do you prefer?

I don't know my teachers method. I don't know which method I use but if I bring down t-25=0 wouldn't 5 be 25?
My teacher got a totally different answer because of the (5t+2)
i dont know how she got that

Originally Posted by buck

I don't know which method I use but if I bring down t-25=0 wouldn't 5 be 25?

you may have to clarify further what you mean by this.

I would solve using the quadratic formula