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:

📰 Never Stop Playing 2Games.io – These Hidden Features Will Blow Your Mind! 📰 You WERE Winging It—Now Marco Polo’s ‘2k24’ Explodes With Hidden Secrets! 📰 2k24 Revealed: The Game That Changed Gaming Forever (Spoiler Alert!) 📰 You Wont Believe How 7X4 Changed Everything About Your Life 721919 📰 Shocked Youre Not Using This Microsoft Volume Licensing Service Center Tool Heres How 1929013 📰 Power Automate Extract Text From Pdf 7962798 📰 Master Iobservation See What Experts Never Want You To Know 5632329 📰 Sweat Now Shine Later This Pro Sportswear Is Changing How Athletes Train Forever 6639549 📰 Can You Record A Phone Call On Iphone 8553677 📰 Dr Phill 7430577 📰 Unleash Your Genius With These Mind Blowing Cool Drawing Ideas 4317068 📰 Unlock Massive Returns My Insider Aol Stock Portfolio Strategy You Need To Try 9421008 📰 Stop Waiting For Loans How These Money Lending Apps Pay You In Hours Now 2192913 📰 Stop Blending Elevate Your Content With Perfect Fruit Clipart Clips 862726 📰 Unlock Hidden Patterns How Sql Datediff Revolutionizes Data Comparisons 9244260 📰 Peopleof Exposed Revealing The Untold Legends Behind Viral Fame 3946825 📰 Martinellis Silent Apple Juice Holds A Hidden Power Every Sip Holds A Surprise 9891883 📰 Zip Code San Antonio Texas Usa 9207510

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.