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:

📰 Marvel Rival Mods 📰 Madame Masque 📰 All Hallows Eve Fallout 4 📰 Ucf Tuition 844785 📰 You Wont Believe Whats Hidden Inside My Filesclick To Discover 2778912 📰 Fun Free Things To Do 6121123 📰 Audio Dedupe 474251 📰 Dont Miss How Fidelitys High Yield Bonds Are Beating Fear In The Market 3201790 📰 Nyse Ryn Mistery Revealed How A Single Trade Changed The Market Forever 8714034 📰 Mouthwashing Free Download 6894629 📰 Adidas Stock Explodesyou Wont Believe How Much Its Surged This Week 704661 📰 This Tiger Drawing Will Blow Your Mindmaster It Like A Pro 1681053 📰 The Forbidden Map Revealed In Pirates Of The Caribbean 2 That Changes Everything 9718703 📰 Sonesta Emeryville San Francisco Bay Bridge 308152 📰 Inside The Secret Indigo Credit Card Login Portal Youve Been Ignoring 3046195 📰 L Methylfolate Supplements 4367453 📰 Unlock Hidden Features In Textapp You Didnt Know Existed 6726833 📰 Shabbat Shalom Meaning Secrets You Didnt Knowdownload Its Power Instantly 3597536

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.