Let's complete the square (as this is actually how the quadratic formula is derived)
-4x^2+16x-24=0 make the leading coefficient equal to 1 by dividing the entire equation by -4
x^2-4x+6=0, move the constant to the other side by subtracting 6 from both sides
x^2-4x=-6, halve the linear coefficient, square it, then add it to both sides, (-4/2)^2=4
x^2-4x+4=-2 now the left side is a perfect square
(x-2)^2=-2 now take the square root of both sides
x-2=±i√2 note the imaginary unit i as there is no real square root of -2, now add 2 to both sides
x=2±i√2 so the factored quadratic is:
(x+2-i√2)(x+2+i√2)
Note that these are not real factors, if you were to graph the original equation, it will never intersect with the x-axis...