Can anyone help me understand how to do this?

Question

Factoring each polynomial
x^2+5ax+6a^2
and
solve each equation
a^2+a=20
I am so lost with this one I can not grab how you get a number from this.
thanks for trying who ever you may be

Answer 1

X^2+5aX+6a^2

splitting the middle term as

X^2+3ax+2aX+6ax^2
------ ---------

take common factor from 2 terms,sequentially as
X(X+3a)+2a(X+3a)

(X+2a) (X+3a) answer is x=-2a ;X=-3a

Question 2: a^2+a-20=0
a^2+5a-4a-20=0

a(a+5)-4(a+5)

(a+5) (a-4)=0

or a=-5 ; +4

both are factorised using splitting the middle term method