The equation displayed in the image is:

$2y - 3 = 12y + 27$

Let's solve this equation step by step.

Step 1: Simplify both sides

First, subtract $12y$ from both sides to bring all terms involving $y$ to the left side:

$2y - 12y - 3 = 27$

This simplifies to:

$-10y - 3 = 27$

Step 2: Isolate the variable $y$

Next, add 3 to both sides:

$-10y = 30$

Step 3: Solve for $y$

Divide both sides by $-10$:

$y = \frac{30}{-10} = -3$

Step 4: Verify the solution

Substitute $y = -3$ into the original equation to check if it holds true:

$2(-3) - 3 = 12(-3) + 27$

Simplifying both sides:

$-6 - 3 = -36 + 27$

$-9 = -9$

Since both sides are equal, the solution is correct.

Conclusion:

The solution set is $\{-3\}$, which corresponds to option A.

Would you like further clarification or details on any of these steps?

Here are 5 related questions:

1. How would the solution change if the equation was $2y - 3 = 12y - 27$?
2. What is the solution if the right-hand side of the equation includes a constant term of 0?
3. How do you solve an equation where the variable appears on both sides with fractions?
4. How does one verify a solution in more complex equations?
5. How would the equation behave if the coefficients were non-integer values?

Tip: Always check your solution by substituting it back into the original equation to ensure accuracy.