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The solutions to the equation \( 2x^3 + 5x^2 - 4x - 12 = 0 \) are:

\[
x = -2 \quad \text{and} \quad x = \frac{3}{2}.
\]

Would you like more details on the solution process, or do you have any questions? 

Here are some follow-up questions to consider:
1. How do we solve cubic equations step by step?
2. What is the significance of rational roots in solving polynomials?
3. How can the Rational Root Theorem help in finding potential solutions?
4. How does factoring a cubic polynomial work after identifying roots?
5. What methods are available if a polynomial equation does not have rational roots?

**Tip:** For polynomials with degree 3 or higher, finding one real root (using synthetic division or trial methods like the Rational Root Theorem) simplifies the problem greatly!

Solve this equation: 2x^3 + 5x^2 - 4x - 12 = 0

Learn how to solve the cubic equation 2x^3 + 5x^2 - 4x - 12 = 0 step by step. This solution involves factoring and applying the Rational Root Theorem. Suitable for high school students (Grades 10-12).

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