Factorize the expression: 2y2 - 5ya - 3a2

The expression is in the form $Ay^2 + By + C$, where $A=2$, $B=-5a$, and $C=-3a^2$.

We need two numbers that multiply to $(2)(-3a^2) = -6a^2$ and add up to $-5a$.
These two numbers are $a$ and $-6a$.
($a \times -6a = -6a^2$ and $a + (-6a) = -5a$)

Group the first two terms and the last two terms:

Factor out the common term from each group:

The common binomial factor is $(2y + a)$.