To simplify the expression \((7x^2 - 6x + 2) - (4x - 8) + (-6x^2 + 3x)\), let's first distribute the negative sign in the second term and then combine like terms.
-
Distribute the negative sign: \[ (7x^2 - 6x + 2) - 4x + 8 + (-6x^2 + 3x) \]
-
Combine all terms: \[ 7x^2 - 6x + 2 - 4x + 8 - 6x^2 + 3x \]
-
Group like terms (i.e., \(x^2\) terms, \(x\) terms, and constant terms):
- \(x^2\) terms: \(7x^2 - 6x^2 = (7 - 6)x^2 = 1x^2 = x^2\)
- \(x\) terms: \(-6x - 4x + 3x = (-6 - 4 + 3)x = -7x\)
- Constant terms: \(2 + 8 = 10\)
-
Combine the results: \[ x^2 - 7x + 10 \]
Hence, the simplified expression is: \[ \boxed{x^2 - 7x + 10} \]