The value of k is 36
Solution:
Given equation is:
[tex](8x+3k)(9x-2) = 0[/tex]
Equate each factor to zero and solve for x
[tex]8x + 3k = 0\\\\8x = -3k\\\\Divide\ both\ sides\ by\ 8\\\\x = \frac{-3k}{8}[/tex]
Also,
[tex]9x-2=0\\\\9x = 2\\\\Divide\ both\ sides\ by\ 9\\\\x = \frac{2}{9}[/tex]
Given that product of all solutions is -3
Therefore,
[tex]\frac{-3k}{8} \times \frac{2}{9} = -3\\\\\frac{-k}{12} = -3\\\\k = 3 \times 12\\\\k = 36[/tex]
Thus k is 36
