How would you solve the following equation by factoring?

Question

I have 4x²-27x+18=0

While I know you usually begin by finding a factor of all three numbers, there is not one for these numbers. How would I continue?

Answer 1

4x^2-27x+18=0

4*18=2*2*2*3*3=(2*2*2*3)*3 =24*3 and 24+3=27

(4x )(x ) so far

(4x 3)(x 6) so far

(4x-3)(x-6)=0

4x-3=0

4x=3

x=3/4

x-6=0

x=6

Answer 2

4x²-27x+18=0

(4x - 3)(x - 6) = 0

how I did it:

I tested the possible factors of 18, realizing that for the b term to be negative and the c term to be positive, the factors of 18 would both be negative. I used -3 and -6. Then, I saw that 4 x -6 = -24, and, -24 + -3 = 27.