Let's simplify the expression:

$7x - 9x - 15 + 12x$

Combine the like terms involving $x$:

$(7x - 9x + 12x) - 15$

Calculate the coefficients:

$(7 - 9 + 12)x - 15 = 10x - 15$

So, the simplified form of the expression is:

$\boxed{10x - 15}$

Would you like more details or have any questions?

Here are some related questions to explore:

1. How do you solve an equation with multiple terms?
2. What are like terms, and why are they combined in algebra?
3. How do you factor expressions like $10x - 15$?
4. What is the process of simplifying more complex algebraic expressions?
5. How can you solve for $x$ if this expression is set equal to a number?

Tip: Always look for like terms in an expression to simplify it easily!