To simplify the expression $(7x^2 - 6x + 2) - (4x - 8) + (-6x^2 + 3x)$, follow these steps:

1. Distribute any subtraction across the terms: $7x^2 - 6x + 2 - 4x + 8 + (-6x^2 + 3x)$

2. Combine like terms:

   • Combine the $x^2$ terms: $7x^2 - 6x^2 = 1x^2$
   • Combine the $x$ terms: $-6x - 4x + 3x = -7x$
   • Combine the constant terms: $2 + 8 = 10$

3. The simplified expression is: $x^2 - 7x + 10$

Would you like to know more details about any step or have any questions?

Here are 5 related questions to explore:

1. How do you factor the expression $x^2 - 7x + 10$?
2. What are the roots of the quadratic equation $x^2 - 7x + 10 = 0$?
3. How does combining like terms work in polynomial expressions?
4. Can you explain the process of distributing a negative sign across an expression?
5. How do you expand and simplify polynomial expressions?

Tip: Always keep track of your signs when simplifying expressions to avoid mistakes.