y = 3(2)^2 - 12(2) + 15 = 12 - 24 + 15 = 3

February 22, 2026

Understanding the Quadratic Equation: Simplifying y = 3(2)² – 12(2) + 15 Step by Step

Solving quadratic equations is a foundational skill in algebra, and one that often causes confusion—even for experienced learners. In this article, we break down the equation:

y = 3(2)² – 12(2) + 15 and simplify it step by step to reveal why it finally simplifies to y = 3. Whether you're studying algebra, teacher, or self-learner, understanding how to evaluate and simplify expressions—especially quadratic forms—is essential for mastering more complex math concepts.

What Is the Given Equation?

Our starting equation is: y = 3(2)² – 12(2) + 15

At first glance, this seems like a standard quadratic expression—but in this case, we’ll treat it like a linear evaluation problem since no variable “y” is isolated as the subject. But the challenge lies not in solving for a variable, but in correctly evaluating the expression using order of operations (PEMDAS/BODMAS).

Step 1: Apply the Exponent First

Because of the exponent (2) in (2)², we apply the P (Parentheses) rule in sequence with E (Exponents): (2)² = 4

Now substitute: y = 3 × 4 – 12 × 2 + 15

Step 2: Perform Multiplication from Left to Right

Multiplication comes before addition and subtraction, per BODMAS/PEMDAS:

First term: 3 × 4 = 12
Second term: 12 × 2 = 24

Now substitute: y = 12 – 24 + 15

Step 3: Evaluate from Left to Right (Addition and Subtraction)

We proceed left to right:

12 – 24 = –12
Then: –12 + 15 = 3

Final Result:

y = 3

Why This Process Matters

Understanding this step-by-step breakdown is crucial for:

Mastering algebraic simplification, a foundation for solving equations.
Avoiding common errors in calculation order, especially when exponents and multiplication are involved.
Applying logical thinking to more complex expressions and real-world problem-solving.

A Quick Recap Formula

For clarity, the full simplification is: y = 3(2)² – 12(2) + 15 = 3×4 – 24 + 15 = 12 – 24 + 15 = –12 + 15 = 3

Practice Tip

Try evaluating similar expressions: Example: y = 2(3)² – 5(3) + 10 = 2×9 – 15 + 10 = 18 – 15 + 10 = 13

Keep practicing with parentheses and exponents — precision is key!

Summary

Evaluating y = 3(2)² – 12(2) + 15 simplifies neatly to y = 3 through careful application of order of operations—exponents first, then multiplication, followed by left-to-right addition and subtraction. This core algebraic process strengthens foundational math skills essential for higher-level learning.

Key Takeaways:

Always apply exponents before multiplication
Follow the order of operations (PEMDAS/BODMAS) rigorously
Simplify step by step to avoid compounding errors

Start mastering your quadratics—and any algebra—today! For more lessons like this, subscribe and deepen your math mastery.