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.

$x^2 + 2x - 3x - 6 = 0 \\$

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:

📰 How the Fourth Hokage Changed Ninja History Forever—Shocking Details Revealed! 📰 You’re Not Ready for This: The Untold Truth of the Fourth Hokage’s Shocking Rise! 📰 Discover the Secret Behind the 4 Leaf Clover 4 – You Won’t Believe How This Symbol Changes Your Luck! 📰 The Secret Tap Tempo Everyones Using But Never Talk About 📰 The Secret Tba You Cant Ignore 📰 The Secret Teamcare Trick Everyone Fails To Use Before Its Too Late 📰 The Secret Tech Cu Discovery You Needed But Didnt Know You Wanted Yet 📰 The Secret Technique That Makes Your Star Drawings Unbelievably Real 📰 The Secret Tennis Link Hinted At A Hidden Betrayalnow Coming Out 📰 The Secret Texas Toll Tag That Is Costing Drivers More Than You Think 📰 The Secret That Changed Everything About The 80S Show Forever 📰 The Secret That Makes Divorce Feel Like Freedom Not Failure 📰 The Secret That Third Rock From The Sun Holds About The Disease Hiding In Plain Sight 📰 The Secret That Unlocked The Wall 2017 Forever 📰 The Secret They Dont Want You To Hear About Straighttalk 📰 The Secret They Hide About The Change Up That No One Talks About 📰 The Secret Thi Does That Before Every Major Breakthrough 📰 The Secret Third Eye Revealed How It Unlocks Mystical Awareness Tonight

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.