Let z = 3x +2. Then the equivalent quadratic equation can be written as
z² +7z -8 = 0
_____
This can be factored as
(z -1)(z +8) = 0
which has solutions
z = {1, -8}.
Then the corresponding values of x are found from
z = 3x +2
z -2 = 3x
(z -2)/3 = x
For z = 1,
(1 -2)/3 = x = -1/3
For z = -8
(-8 -2)/3 = x = -10/3