Simplifying the Expression: (−x2−3x+3)−(−x2−9x+6)
This problem involves subtracting two polynomials. To simplify this expression, we need to follow these steps:

Distribute the negative sign: The negative sign in front of the second set of parentheses means we multiply each term inside the parentheses by 1.
This gives us: (−x2−3x+3) + (x2 + 9x  6)

Combine like terms: Identify terms with the same variables and exponents and combine their coefficients.
 x2 terms: x2 + x2 = 0
 x terms: 3x + 9x = 6x
 Constant terms: 3  6 = 3

Write the simplified expression: After combining like terms, the simplified expression is: 6x  3
Therefore, the simplified form of (−x2−3x+3)−(−x2−9x+6) is 6x  3.