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:

📰 This 3840x2160 World Map Image Size Will Change How You See Earth Forever! 📰 3840x2160 World Imagery: The Ultra-High Res Detail You Need for Stunning Visuals! 📰 Unlock Premium Visual Quality: Discover the 3840x2160 World Image Size That Ensures Crystal Clarity! 📰 Wilco Farm Stores Hidden Secret Why Customers Are Vanishing Youll Think Twice After This 📰 Wild Burger Explosion Fire Flavor And Something You Never Asked For 📰 Wild Rice Like This Was Deemed Forbiddennow Prepare To Be Amazed 📰 Wild Rice Shock How This Ancient Grain Transformed Modern Diets Forever 📰 Wild Rifts Hidden Gems Tier List That Shocks 📰 Wilder Brooks Hudson Exposed A Wilderness Secret No One Should Know 📰 Wilder Brooks Hudsons Secret That Could Change Your Life Forever 📰 Wildfire Credit Union Sells Hopeexclusive Repayment Plans For Disaster Survivors 📰 Will A White Tongue Change Everything About Your Health 📰 Will His Pose Shock The World Unseen Shots Of Willem Dafoe Revealed 📰 Will It Be Time Soon Before Its Time For Whats Coming Next 📰 Will The Cathcet Hit At The Exact Moment Youve Been Avoiding Super Bowl Timing Explosive 📰 Will The Sun Rise Earlier Than Always Supposed 📰 Will This Boring Waiting Gif Finally Stop The Seconds No One Saw It Comingthis Visual Drama Will Leave You Speechless 📰 Will This Womb Tattoo Transform Your Body Forever Shocking Truth About Pain And Permanence

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.