How do you solve $2x-3=3x+6$?

Hint: We have a linear equation in one variable. We will first rearrange the equation so that we have the constant terms on one side of the equation and the variable terms on the other side. Then we will simplify the equation by doing the arithmetic operations in the equation. We will divide the constant term by the coefficient of the variable and obtain the solution.

Complete step-by-step solution:
The given equation is $2x-3=3x+6$. Now, we will rearrange the equation by collecting the variable terms on one side of the equation and the constant terms on the other side of the equation. So, we get the following equation,
$2x-3x=6+3$
Now, we have to simplify the above equation. On the left hand side, we have the subtraction operation. We will subtract the second term from the first term. We obtain the following equation,
$-x=6+3$
Next, on the right hand side, we have the addition operation. We will add the two constant terms and obtain the following equation,
$-x=9$
Now, we will multiply both sides by $-1$ and get the following,
$x=-9$
This is the solution of the given linear equation.

Note: We should be careful with the signs of the terms while shifting them from one side of the equation to the other. The highest degree of the given equation is 1. Hence, it is a linear equation. If the highest degree of an equation is 2, it is called a quadratic equation. If the highest degree of an equation is 3, then it is called the cubic equation.