$\large ax^2 + bx +c=a(x-r1)(x-r2)$

where

$r1,r2=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

in this case

$r1=\dfrac 3 4, ~r2=\dfrac 1 2, ~a=8$

$8\left(x-\dfrac 3 4\right)\left(x - \dfrac 1 2\right)=$

$8\left(x^2-\dfrac{5x}{4}+\dfrac 3 8\right)=$

$8x^2-10x+3$

and of course you can distribute the factor of 8 between the 2 factors to get rid of fractions as

$8\left(x-\dfrac 3 4\right)\left(x - \dfrac 1 2\right)=$

$4\left(x-\dfrac 3 4\right) \cdot 2\left(x - \dfrac 1 2\right) = $

$(4x-3)(2x-1)$

This isn't generally the fastest way to factor a polynomial but it will always work when all else fails.