To solve the equation x^3 + x^2 = 9x + 9, first, move all terms to one side of the equation:
x^3 + x^2 - 9x - 9 = 0

Now, factor out an x:
x(x^2 + x - 9) = 0

Next, factor the quadratic equation inside the parentheses:
x(x + 3)(x - 3) = 0

So the solutions for x are x = 0, x = -3, and x = 3.

To solve the equation 3x^2 - 3x = 0, factor out a common factor of 3x:
3x(x - 1) = 0

Therefore, the solutions for x are x = 0 and x = 1.

For the equation 3x^2 - 6x + c = 0, we can use the quadratic formula to solve for x. The quadratic formula is:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, the coefficients are a = 3, b = -6, and c = c. Plugging these values into the formula, we get:

x = (6 ± sqrt((-6)^2 - 43c)) / 2*3
x = (6 ± sqrt(36 - 12c)) / 6
x = (6 ± sqrt(36 - 12c)) / 6

These are the two solutions for x in terms of c.