For ease in factoring this equation, multiply all terms by the LCD (which is 3*4, or 12) to remove the fractions:
16x^2 - 24x + 9 = 0
From here the factoring process is straightforward. The square root of 16x^2 is 4x and that of 9 is 3, so try this set of factors:
(4x-3)(4x-3) = 0. This does indeed multiply out to 16x^2 - 24x + 9 = 0, which is equivalent to the given 4/3 x^2 - 2x + 3/4 = 0.
