Let's simplify the expression step by step. The expression we need to simplify is:
\[ (7x^2 - 6x + 2) - (4x - 8) + (-6x^2 + 3x) \]
- Distribute the negative sign in front of the second group:
\[ (7x^2 - 6x + 2) - 4x + 8 + (-6x^2 + 3x) \]
Which simplifies to:
\[ 7x^2 - 6x + 2 - 4x + 8 - 6x^2 + 3x \]
- Combine like terms:
-
For \(x^2\) terms: \[ 7x^2 - 6x^2 = (7 - 6)x^2 = 1x^2 \text{ or simply } x^2 \]
-
For \(x\) terms: \[ -6x - 4x + 3x = (-6 - 4 + 3)x = -7x \]
-
For constant terms: \[ 2 + 8 = 10 \]
- Combine all simplified terms:
Putting it all together, we have:
\[ x^2 - 7x + 10 \]
Thus, the completely simplified expression is:
\[ \boxed{x^2 - 7x + 10} \]