To solve the inequality \( x^3 - 5x^2 - 6x < 0 \), we can follow these steps:

### Step 1: Factor the expression on the left-hand side
We can start by factoring the cubic expression:
\[
x^3 - 5x^2 - 6x = x(x^2 - 5x - 6)
\]
Next, factor the quadratic \( x^2 - 5x - 6 \):
\[
x^2 - 5x - 6 = (x - 6)(x + 1)
\]
So the inequality becomes:
\

Learn how to solve the cubic inequality x^3 - 5x^2 - 6x < 0 with step-by-step factoring and applying the zero-product property. This problem introduces important algebraic concepts like cubic polynomials and inequalities, suitable for students in Grades 9-12.

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Solution

Step 1: Factor the expression on the left-hand side

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