Question 367588
{{{4x^2 - 12x + 9 > 0 }}} is the same as {{{(2x-3)^2 >0}}}.  All real numbers will satisfy this except x = 3/2, when it is zero.  Thus the solution set is ({{{-infinity}}}, 3/2)U(3/2, {{{infinity}}}).

4x^2 - 3x - 6 = 0 
Check the discriminant:{{{b^2-4*a*c = (-3)^2 - 4*4*-6 = 9 +96=105}}}.  The value of the discriminant is positive but is not a perfect square, so the quadratic expression cannot be factored into linear factors with rational coefficients.