The equation given is:

$-2x + 6 = 5x + 15$

Let's solve for $x$:

1. First, move all the terms involving $x$ to one side. Subtract $5x$ from both sides:

$-2x - 5x + 6 = 15$

This simplifies to:

$-7x + 6 = 15$

2. Next, move the constant term $6$ to the other side by subtracting 6 from both sides:

$-7x = 15 - 6$

Simplifying:

$-7x = 9$

3. Finally, solve for $x$ by dividing both sides by $-7$:

$x = \frac{9}{-7} = -\frac{9}{7}$

Thus, the solution is:

$x = -\frac{9}{7}$

Would you like more details or have any questions? Here are some follow-up questions you might find helpful:

1. How do we isolate variables when solving linear equations?
2. What happens if there are no solutions to a linear equation?
3. How can this method be applied to equations with fractions?
4. How do we check if the solution is correct?
5. What if the coefficients in front of $x$ were decimals?

Tip: Always verify your solution by plugging it back into the original equation to ensure both sides are equal.