determine the values of$\displaystyle a,b,c$ such that the vector vield

$\displaystyle F = (2x +ay -3z)i +(4x-y-bz)j +(cx-3y+z)k$

is irrotational i.e. $\displaystyle \nabla \wedge F =0$

my attempt

$\displaystyle \nabla \wedge F = (-3+b) +(-3-c) +(4-a) = 0$

which is simplified to

$\displaystyle b-c+a =2$

what other formulas can i use to find $\displaystyle a,b,c$?