How do I solve for b? 
16b-squared - 9 = 0

16b2 - 9 = 0

Two ways.  Factoring method:

16b2 - 9 = 0

can be written as

(4b)2 - 32 = 0

This is the difference of two perfect squares. The difference of two perfect
squares factors into the product of the sum and differencve of the two square
roots.

(4b - 3)(4b + 3) = 0

Now use the zero-factor principle, which is to put " = 0 " after each of those
two parenthetical factors and solve for the two answers:

4b - 3 = 0                4b + 3 = 0
    4b = 3                    4b = -3 
     b = 3/4                   b = -3/4

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Second way:  Taking square roots:

16b2 - 9 = 0

Add 9 to both sides

16b2 = 9

Take the square roots of both sides, remembering that there are
two square roots.
                         _
square roots of 16b2 = ±Ö9
      
                  4b = ±3

                   b = ±3/4

Edwin
AnlytcPhil@aol.com