-d = 3 sqrt d - 2

a) {3}
b) none
c) {6}
d) {3,6}

To find the solution to the equation -d = 3sqrt(d) - 2, we can follow these steps:

1. Start by isolating the square root term on one side of the equation. To do this, add "d" to both sides:
-d + d = 3sqrt(d) - 2 + d
0 = 3sqrt(d) - 2 + d

2. Move the constant term (-2) to the left-hand side of the equation by adding 2 to both sides:
0 + 2 = 3sqrt(d) - 2 + d + 2
2 = 3sqrt(d) + d

3. Now, we want to isolate the square root term. Move the "d" term to the right-hand side of the equation by subtracting "d" from both sides:
2 - d = 3sqrt(d) + d - d
2 - d = 3sqrt(d)

4. Next, divide both sides of the equation by 3:
(2 - d)/3 = (3sqrt(d))/3
(2 - d)/3 = sqrt(d)

5. Now, we square both sides of the equation to eliminate the square root:
((2 - d)/3)^2 = (sqrt(d))^2
((2 - d)/3)^2 = d

6. Simplify the left-hand side:
(2 - d)^2/3^2 = d
(2 - d)^2/9 = d

7. Expand the square on the left-hand side:
(4 - 4d + d^2)/9 = d

8. Multiply both sides of the equation by 9 to eliminate the fraction:
4 - 4d + d^2 = 9d

9. Rearrange the equation to form a quadratic equation:
d^2 + 9d - 4 = 0

10. Finally, solve the quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, you can factor the quadratic equation as follows:
(d - 3)(d + 6) = 0

11. Set each factor equal to zero:
d - 3 = 0 and d + 6 = 0

12. Solve for 'd':
d = 3 and d = -6

Therefore, the solutions to the equation -d = 3sqrt(d) - 2 are d = 3 and d = -6.

Among the answer choices provided:
a) {3}
b) none
c) {6}
d) {3,6}

The correct answer would be d) {3, 6}, as both d = 3 and d = -6 are solutions to the equation.