Kiara is trying to solve $\sin^2(3x) −\sin(3x) + 0.24 = 0$. She originally makes the substitution $u = 3x$.  

1. What new equation does she get?

   Answer (a):

   $\sin^2(u) − \sin(u) + 0.24 = 0$

2. She decides that she needs to make another substitution using the variable v. What will be a good substitution to make?

   Answer (b):

   Let $v = \sin(u)$.

3. What is Kiara’s equation now?

   Answer (c):

   $v^{2} − v + 0.24 = 0$

4. Solve for $v$.

   Hint (d):

   The equation can be factored. What two numbers have a product of $0.24$ and a sum of $−1$?

5. Solve for $u$.

6. Solve for $x$.