FACTOR

6x^3+2x^2-8x =0
I know the GCF is 2x thus leaving:
2x(3X^2+X-4X)=0 *Stuck after this part*

your factored version is incorrect, the last term is wrong

2x(3x^2 + x - 4) = 0
which factors further to

2x(3x + 4(x - 1) = 0
so ..
x = 0 or x = -4/3 or x = 1