The given expression is:

$-6x^2 + 4 + 7x^2 - 12 - 12x$

We will simplify this expression step by step:

Step 1: Combine like terms

• Combine the $x^2$ terms: $-6x^2 + 7x^2 = (7 - 6)x^2 = x^2$
• Combine the constant terms: $4 - 12 = -8$
• The $x$ term remains as it is: $-12x$

Step 2: Final simplified expression

After combining like terms, the expression becomes: $x^2 - 12x - 8$

Would you like further details or have any questions about the steps?

Here are 5 related questions you might explore:

1. How do you factor a quadratic expression like $x^2 - 12x - 8$?
2. What is the importance of combining like terms in polynomial expressions?
3. How can you solve for $x$ in the equation $x^2 - 12x - 8 = 0$?
4. What are the key properties of quadratic functions and their graphs?
5. How does the degree of a polynomial affect its shape and behavior?

Tip: When simplifying algebraic expressions, always group terms by their powers to make the process easier.