Question

y(y6+y)-5y(y+36)y-55=-100

Answer 1

First you have to expand your terms.

7y^2 - 5y^3 - 180y^2 - 55 = -100

Collect like terms.

-5y^3 -173y^2 = -45

now factor the y^2

y^2(-5y - 173) = -45

There are two solutions to this equation.

y = 0
and
5y + 173 = 45 which yields
y = -25.6

Answer 2

Dan, what you did at the end is totally invalid

Factors can only be set each equal to zero and solved if their product was equal to zero.
Your product of factors was equal to -45

All you have to do is sub in one of your solutions, y = 0, into the equation to see that it cannot possibly work.

The original posters question was typed in a very strange way.
e.g. what does y6 mean, did he/she mean
y^6 or 6y
I see you read it as 6y, if so, then what was the point of the brackets in the first place?