2010/058) factorize: 9x^2 - 9(a + b )x + (2a^2 + 5ab + 2b^2) = 0?

we know

2a^2 + 5ab + 2b^2 = (2a+b)(2b+a)

let s = 2a+b and t = 2b + a

s + t = 3a + 3b

9x^2 - 9(a + b )x + (2a^2 + 5ab + 2b^2)

= 9x^2 - 3(s+t)x + st
= 9x^2 - 3sx - 3tx + st
= 3x(3x-s) - t( 3x -s)
=(3x-s)(3x-t)
= (3x - 2a - b)(3x - a - 2b)