Does anyone know how to factor the expression 2s^2+5s+3. ?

trick to easily factor this is as below
let say = ax^2 + bx + c

first find all the possibilities fo multiply to get a and c(integer only +ve and negative)

a
1x2
2x1

c
1x3
3x1
-1 x -3
-3 x -1

possibility 1:

2x 1
x 3

cross multiply

2x 1 = x * 1 = x
x 3 = 2x * 3 = 6x

total x = x + 6x = 7x
since the middle is 5x then this is wrong

possibility 2:

2x 3 = 2x * 1 = 2x
x 1 = x * 3 = 3x
total x = 2x + 3x = 5x

it is similar to b then the factor is
(2x + 3) (x + 1)

note if question is 2x^2 - 5x + 3 then the answer will be
(2x - 3) (x - 1)

(s+1)(2s+3)

2s^2 + 5s + 3
= 2s^2 + 2s + 3s + 3
= (2s^2 + 2s) + (3s + 3)
= 2s(s + 1) + 3(s + 1)
= (s + 1)(2s + 3)

(2s+3)(s+1)

2s^2+5s+3 = 0
(2s+3)(s+1) = 0
2s+3 =0
s = -3/2
s+1=0
s= -1

answer : s={-3/2,-1)

Step 1,equiting the equation to 0
2s^2 + 5s + 3=0
Step 2 , solve for s
s=[-5 + - (25-24)]/4=-4/4 & -6/4=-1 & -3/2
write 2(s+1)(s+3/2)=(s+1)(2s+3)=2s^2+2s+3s+3=2s^2+5s+3