Find all a for which the lines represented by the equations 2y+3+x=0 and 3y+ax+2=0 are perpendicular
If line l_1 has slope m_1 and line l_2 has slope m_2 then if neither line is vertical then the two line are perpendicular if (m_1)(m_2)=-1.
2y+3+x=0 has slope (-1/2); 3y+ax+2=0 has slope (-a/3).
Now solve for a.