What values of b satisfy 4 times open paren 3 b plus 2 close paren squared is equal to 64 ?

Divide both sides of 4(3b + 2)² = 64 by 4 to get (3b + 2)² = 16. Thus 3b + 2 can equal 4 or −4. Solving gives b = 2/3 or b = −2, so the correct choice is C.

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