To solve the equation $2x - 3 = 5x + 6$, we will go through the following steps:

1. Move all terms involving $x$ to one side of the equation.
   Subtract $5x$ from both sides: $2x - 5x - 3 = 6$ This simplifies to: $-3x - 3 = 6$

2. Move the constant terms to the other side.
   Add 3 to both sides: $-3x = 6 + 3$ Simplifying: $-3x = 9$

3. Solve for $x$.
   Divide both sides by $-3$: $x = \frac{9}{-3} = -3$

Thus, the solution is: $x = -3$

Do you want any more details, or have any questions?

Here are 5 related questions you might find interesting:

1. Solve $4x + 5 = 7x - 10$.
2. Solve $3x - 2 = 2x + 4$.
3. Solve $6x + 3 = 9x - 12$.
4. What happens when there are no solutions in a linear equation?
5. How do you solve equations with fractions, like $\frac{2x}{3} - 1 = x + 4$?

Tip: Always simplify terms involving the variable before isolating the variable on one side of the equation.