(3v + 4)(6 + v)=0
Set each factor equal to zero.
If either of them is zero, then the whole thing is zero.
Zero times anything is zero.
So
3v + 4 = 0 or 6 + v = 0
Subtract 4 from both sides. Subtract 6 from both sides.
3v = -4 v = -6
Divide both sides by 3.
v = -4/3
Test both of these values for v and see that they both work!