Solving the Quadratic Equation: x² + 2x – 3x – 6 = 0

If you’re sitting down to solve the equation x² + 2x – 3x – 6 = 0, you’re already tackling a familiar quadratic expression—but one that may seem tricky at first glance. In this SEO-optimized guide, we’ll walk through simplifying, solving, and understanding the roots of this quadratic equation. Whether you're a high school student, a math enthusiast, or just learning algebra, this article will help you master the problem step by step.

Understanding the Context

What is the Given Equation?

The equation is:
x² + 2x – 3x – 6 = 0

At first glance, combining like terms simplifies the equation significantly.

Image Gallery

Key Insights

Step 1: Simplify the Equation

Combine the linear terms:
2x – 3x = –x

So the equation becomes:
x² – x – 6 = 0

This simplified form, x² – x – 6 = 0, is a standard quadratic equation ready for factoring, completing the square, or using the quadratic formula.

🔗 Related Articles You Might Like:

📰 You Wont Believe the Secret Trick to Select ALL Text in Word! 📰 This Simple Hack Reveals How to Select Every Item in Word Instantly! 📰 Stop Wasting Time: Heres How to Select All in Word Like a Pro! 📰 You Wont Believe How Win 10 Pro Updated10 Shocking Features Inside 7016817 📰 What Does Narcissistic Mean 📰 You Wont Believe Which 2 Letter Words Are Hiding In Plain Sight 8844440 📰 Wells Fargo Customer Service 1800 Number 📰 Annex 51194 📰 Verizon Transfer Data To New Phone 📰 Edesign 9050009 📰 Windows 10 License Scam Heres The Fast Way To Get A Valid License Instantly 5008230 📰 Epic Games Football Manager 📰 Experts Confirm Dolar To Shekel And The Mystery Deepens 📰 Spicy Spicy Chips The Ultimate Burn Thats Taking Social Media By Storm 1934666 📰 Nyt Connections Answers 📰 You Wont Believe What This Killer Did To Its Victims 187612 📰 Who Owns Palantir The Secret Billionaire Behind Its Shocking Rise Revealed 9169034 📰 This Salad Was Bluffingright In Front Of My Eyes What Was Hidden For Days 3877017

Final Thoughts

Step 2: Solve by Factoring

To factor x² – x – 6, look for two numbers that multiply to –6 and add up to –1.
These numbers are –3 and +2, since:
–3 × 2 = –6
–3 + 2 = –1

Thus, the factored form is:
(x – 3)(x + 2) = 0

Step 3: Apply the Zero Product Property

If a product equals zero, one of the factors must be zero:
x – 3 = 0 → x = 3
x + 2 = 0 → x = –2

Solutions:
x = 3
x = –2

Why This Equation Matters

Understanding how to combine like terms and factor quadratics is essential in algebra. The roots x = 3 and x = –2 represent the x-intercepts of the corresponding parabola, helping visualize quadratic behavior in graphs, physics, engineering, and economics.