2(x+1) + 3x = x(x+1) - DevRocket

Solving the Equation: 2(x + 1) + 3x = x(x + 1) – A Comprehensive Guide

📅 May 3, 2026 👤 scraface

May 03, 2026

Solving the Equation: 2(x + 1) + 3x = x(x + 1) – A Comprehensive Guide

When faced with algebraic equations, simplifying both sides and solving for the variable can sometimes seem challenging. One common equation that students and math enthusiasts often explore is:
2(x + 1) + 3x = x(x + 1)

This equation represents a powerful exercise in algebraic manipulation and problem-solving. In this SEO-optimized article, we break down the full process of solving 2(x + 1) + 3x = x(x + 1), providing clear steps, real-world applications, and useful keywords to help improve search visibility for educators and learners alike.

Understanding the Context

Understanding the Equation

The equation
2(x + 1) + 3x = x(x + 1)
contains both linear and quadratic components. The left side involves distribution and combination of like terms, while the right side expands into a polynomial. Solving this equation helps reinforce skills in:

Distributing parentheses
Combining like terms
Expanding binomials
Solving first-degree and quadratic equations

Solved 2x-1 (x+1) | Chegg.com

Image Gallery

Solved 2x-1 (x+1) | Chegg.com

SOLVED:2(x+3)=3(x-1)

Solved: 2) (x+1)/3x-4 - (2x-3)/4+3x [Math]

Solved: |2 x+1|

Solved: the tonowimg expressions 3x(x+1)(x-1) and 2x^2(x-1)(x+3) [algebra]

Key Insights

Step-by-Step Solution

Step 1: Expand Both Sides

Start by expanding each term using algebraic properties.

Left-hand side (LHS):
2(x + 1) + 3x
= 2·x + 2·1 + 3x
= 2x + 2 + 3x
= (2x + 3x) + 2
= 5x + 2

🔗 Related Articles You Might Like:

📰 xr glasses 📰 what is spatial audio 📰 iphone camera dots 📰 Regal Buzz The Hidden Truth No Fame Secrets Ever Revealed 1640932 📰 But Lets Verify All Values 186357 📰 The Ls500 Mystery Solvedwhat Engineers Wont Tell You 4965999 📰 How Mfic Stock Grew Overnightthe Shocking Truth Behind Its Explosive Gain 6807446 📰 Santoras 1586391 📰 Dearborn Schools 4825706 📰 Toddler Snacks Thatll Make Meal Time A Breezeparents Swear By These Yummy Treats 2642791 📰 Bank Of America Travel Reward 440270 📰 You Wont Believe What Happened After Enlink Stock Soared 300 Overnight 2874801 📰 First Calculate The Area Using The Formula A Pi R2 1221973 📰 Zurich Hotels 6093161 📰 Permainan Biliar The Secret Strategy Thats Rewriting Rules In Gaming Finance 4472546 📰 Motorola Stock Surprising Jumpthis Weeks Breakthrough Move You Cant Miss 9859374 📰 Open Starbucks On Christmas 7635054 📰 Sixth Gen Jet Emerges Unseen In Battlesecret Air War Secrets Revealed Inside 5446543

Final Thoughts

Right-hand side (RHS):
x(x + 1)
= x·x + x·1
= x² + x

So the equation becomes:
5x + 2 = x² + x

Step 2: Move All Terms to One Side

To solve for x, bring all terms to one side to form a standard quadratic equation:
x² + x – 5x – 2 = 0
→ x² – 4x – 2 = 0

Step 3: Solve the Quadratic Equation

Use the quadratic formula:
x = [−b ± √(b² – 4ac)] / (2a)
For x² – 4x – 2 = 0,
a = 1, b = –4, c = –2

Calculate the discriminant:
Δ = b² – 4ac = (−4)² – 4(1)(–2) = 16 + 8 = 24

Roots:
x = [4 ± √24] / 2
√24 = √(4×6) = 2√6, so
x = [4 ± 2√6] / 2
→ x = 2 ± √6