Let's expand the terms on both sides of the equation:

32 + (2k+1)^2 = (2k-3)^2
32 + 4k^2 + 4k + 1 = 4k^2 - 12k + 9

Now, let's simplify the equation:

32 + 4k^2 + 4k + 1 = 4k^2 - 12k + 9
4k^2 + 4k + 33 = 4k^2 - 12k + 9

Subtracting 4k^2 from both sides:

4k + 33 = -12k + 9

Now, let's isolate the variable by adding 12k to both sides:

4k + 12k + 33 = 9
16k + 33 = 9

Subtracting 33 from both sides:

16k = -24

Finally, divide by 16 to solve for k:

k = -24/16
k = -3/2

Therefore, the solution to the equation is k = -3/2.