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

Answer Step-by-step explanation:

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

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0