## Factoring the Expression: (x^2+x-6)(2x^2+4x)

This problem involves factoring a product of two quadratic expressions. Let's break it down step-by-step:

### Factoring the Individual Expressions

**1. Factoring (x^2 + x - 6):**

- Find two numbers that multiply to -6 and add up to 1 (the coefficient of the x term).
- These numbers are 3 and -2.
- Therefore, (x^2 + x - 6) factors as
**(x + 3)(x - 2)**.

**2. Factoring (2x^2 + 4x):**

- Factor out the greatest common factor (GCF), which is 2x.
- This leaves us with
**2x(x + 2)**.

### Combining the Factored Expressions

Now we have the factored form of the original expression:

**(x^2 + x - 6)(2x^2 + 4x) = (x + 3)(x - 2) * 2x(x + 2)**

### Simplifying the Expression

We can further simplify the expression by rearranging the terms:

**(x + 3)(x - 2) * 2x(x + 2) = 2x(x + 3)(x - 2)(x + 2)**

This is the fully factored form of the original expression.

### Summary

By factoring each quadratic expression individually and then combining them, we were able to completely factor the expression (x^2 + x - 6)(2x^2 + 4x) into:

**2x(x + 3)(x - 2)(x + 2)**