20x^2 – 37x – 18 factor completely????

20x^2-37x-18
=20x^2+8x-45x-18
=20x^2-45x+8x-18
=5x(4x-9)+2(4x-9)
=(4x-9)(5x+2)

20x^2 – 37x – 18
Factors of 20x^2 = 1x,20x; 4x,5x (Let us take 4x, 5x)
Factors of 18 = 1,18; 2,9; 3,6 (Let us take 9, 2)
Since the Constant is -ve we have two signs
( 4x - 9) (5x + 2)
(Multiplying the inside (5 x 9 = 45) and outside (4 x 2 = 8)
45 - 8 = 37 (co-efficient of x)
THE FACTORS ARE (4x - 9) (5x + 2)

20x^2 - 37x - 18
= 20x^2 + 8x - 45x - 18
= (20x^2 + 8x) - (45x + 18)
= 4x(5x + 2) - 9(5x + 2)
= (5x + 2)(4x - 9)

(5x + 2)(4x - 9)

The old "guess and check" really comes in handy. You need two factors of 20 and two factors of 18.

20= 2*2*5
18=2*3*3

Using these it looks like 4&5 and 2&9 work. So,

(4x - 9)(5x + 2) = 0

4x - 9 = 0
4x = 9
x = 9/4

5x + 2 = 0
5x = -2
x = -2/5

Have a good day!

( 4x - 9 ) ( 5x + 2 )