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10y^2 - 9y = 1
let's bring the one over by subtracting it from both sides and get
10y^2 - 9y - 1 = 0
Now let's set up our binomial factors...
( )( ) = 0
We look at the second sign and know our factors' signs are different...
( + )( - ) = 0
The we multiply the first and last coefficients and say
"We need factors of ten that have a difference of 9."
Well -10 and +1 fit the bill...
(10y + 1)(y - 1) = 0
y = -1/10 and y = 1