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:

📰 5Certainly! Here are A train travels from City A to City B, a distance of 300 miles, at an average speed of 75 miles per hour. On the return trip, due to heavy traffic, it travels at an average speed of 50 miles per hour. What is the average speed for the entire round trip? 📰 The time to travel from City A to City B is 300 / 75 = 4 hours. 📰 The time to return is 300 / 50 = 6 hours. 📰 The Burger Temp Thats Taking The Food Industry By Storm Discover It Now 📰 The Burger Temps Just Broke Records Is Your Burger Ready 📰 The Burgundy Bag Thats Taking Instagram By Stormsee How Its Changing Trends 📰 The Burgundy Dress Thats Taking Fashion By Stormdont Miss This Hidden Gem 📰 The Burmy Aesthetic Is Taking Over Real People Are Using It Everyday 📰 The Butterfly Dress Thats Taking Social Media By Stormshop Now Before Its Gone 📰 The Butterfly Emoji Is Taking Over Conversationsare You Using It Right 📰 The C In Cursive That Everyone Overlooks Turn It Into Art Today 📰 The C Major Chord The Ultimate Key That Flips Piano Pros Skills Overnight 📰 The C Minor Chord You Never Knew Could Turn Your Songs Into Masterpieces Heres Why 📰 The C Table Hacked Perfect Size Mind Blowing Design That Dominates Every Room 📰 The Caesar Cut Haircut Is Taking Over 2025 Watch Grogen Marys Latest Trend 📰 The Cafe Astrology Cafe Where Coffee And Cosmic Energy Mix Deliciously 📰 The Cafeteria Menu Thatll Have You Arriving Early And Ordering Twice 📰 The California Flags Shockingly Unhinged Design Will Blow Your Mind

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.