14y^2 - 41y+27 Factor the trinomial

Here's the trick:

Multiply 14 and 27. The answer is 378.
Find two number whose product is also 378, but whose sum is -41.
Those two numbers are NEGATIVE 14 and NEGATIVE 27.

Separate the -41y into -14y and -27y.

14y² - 14y - 27y + 27

Factor by grouping

14y(y - 1) - 27(y - 1)

Since 14y and -27 are both multiplied by (y - 1), you can combine them.

(14y - 27)(y - 1)

(-1 + y) (-27 + 14 y)

(7y - 9)(2y - 3)

14y^2 - 41y+27
(7y-9)(2y-3)=0
y=9/7
y=3/2