Expand: 3x - 12 + 2x = 5x + 6

February 22, 2026

How to Solve the Equation: 3x - 12 + 2x = 5x + 6

Solve algebraic expressions like 3x - 12 + 2x = 5x + 6 with confidence—this step-by-step guide breaks down the process of expanding, simplifying, and isolating variables to find the value of x. Whether you're a student learning algebra or seeking a refresher, understanding how to expand and simplify equations is essential for success in math and related STEM fields.

Understanding the Equation

At its core, the equation 3x - 12 + 2x = 5x + 6 requires simplifying both sides using the distributive and combining like terms. Expanding means identifying any parentheses (though none are present here), rearranging terms, and combining variables and constants.

Step 1: Combine Like Terms on Each Side

Start with the left side: 3x + 2x - 12 This simplifies to: 5x - 12

Now the right side: 5x + 6 (already simplified)

Now rewrite the equation: 5x - 12 = 5x + 6

Step 2: Expand and Simplify

In this case, no expansion is needed beyond combining like terms. The equation now matches: 5x - 12 = 5x + 6

Subtract 5x from both sides: -12 = 6

Step 3: Analyze and Interpret

This result, -12 = 6, is a contradiction—meaning there is no solution that satisfies the original equation. Both sides simplify to unlike constants, so no value of x can make the equation true.

Why This Matters (Real-World Application)

Understanding why equations have no solution helps in many areas, from optimizing business models to debugging scientific experiments. Recognizing when equations resolve to contradictions strengthens problem-solving skills in algebra and beyond.

Summary: Key Takeaways

Expand means simplifying expressions by removing parentheses (here implicitly, by combining like terms).
Combine 3x + 2x = 5x and constants -12 + 0 = -12.
On both sides, the coefficient of x is 5x; subtracting gives -12 = 6.
The result is a contradiction—no solution exists.
Use this logic to verify logical consistency in algebraic expressions.

Practice Tip

Try solving similar equations:

2x + 8 = 5x - 1 → Expand, combine terms, isolate x
4x - 7 = 2x + 5 → Follow inverse steps
Check for no-solution cases: variables cancel but constants disagree

Final Thought

Mastering algebra starts with understanding equation expansion and simplification. When equations like 3x - 12 + 2x = 5x + 6 yield contradictions, you learn not just how to solve—but when no solution exists. This mindset builds deep mathematical reasoning and confidence.

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