To solve the equation (9-x^2)(2x+1) = 0, we can set each factor equal to zero and solve for x.

Setting 9-x^2 = 0:
x^2 = 9
Taking the square root of both sides:
x = ±3

Setting 2x+1 = 0:
2x = -1
Dividing both sides by 2:
x = -1/2

Therefore, the solutions to the equation are x = 3, x = -3, and x = -1/2.