Use substitution to write an equivalent quadratic equation. (3x + 2)2 + 7(3x + 2) – 8 = 0

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

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