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The distributive property is a fundamental concept in algebra that helps us simplify expressions and solve equations. It allows you to multiply a single term by each term inside a parenthesis. Think of it as distributing the multiplication over addition or subtraction.
In our example equation, we applied the distributive property on both sides:
Left Side: $$3(2x - 9) = 6x - 27$$
Right Side: $$6(x - 5) = 6x - 30$$
The distributive property helps to see the equation more clearly without parentheses, making it easier to combine like terms or proceed with further algebraic steps.

Like terms are terms that have the same variables raised to the same power. Combining like terms simplifies the equation and helps to isolate the variable.
In the given equation after using the distributive property, we get:
$$6x - 27 = 6x - 30$$
Here, 6x on both sides are like terms. When we subtract 6x from both sides to combine like terms, we are left with a simplified comparison between constants:
$$-27 = -30$$
Always arrange the terms to align like terms for clarity and simplicity in solving equations.

Sometimes, an equation results in a statement that is always false, indicating that there is no solution to the equation. This usually happens when all variable terms cancel out, leaving a false numerical statement.
In this case, after simplifying both sides and combining like terms, we end up with the equation:
$$-27 = -30$$
This statement is never true, hence the equation has no solution. Understanding this concept helps in quickly identifying equations that do not have any solutions and saves time during problem-solving.
Remember, if you end up with a true statement (like 0 = 0), it means the equation has an infinite number of solutions. But a false statement like our example means no solution.