It looks like you are trying to work with the equation \( 3x(x^2 - 5x + 7) < 0 \) or something similar. If that's the case, let’s solve the inequality step-by-step.

1. **Expanding the expression**:
The first step is to express the term clearly, but we can also analyze the factors. We have:
\[
3x(x^2 - 5x + 7)
\]

2. **Identify the roots of the quadratic**:
To better understand when this expression is less than zero, we first find the roots of the quadratic \( x^2 - 5x + 7 \). We use the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
where \( a = 1, b = -5, \) and \( c = 7 \).
\[
x = \frac{5 \pm \sqrt{(-5)^2 - 4 \cdot 1 \cdot 7}}{2 \cdot 1} = \frac{5 \pm \sqrt{25 - 28}}{2} = \frac{5 \pm \sqrt{-3}}{2}
\]
The expression under the square root is negative, indicating that there are no real roots for \( x^2 - 5x + 7 \).

3. **Determine the sign of the quadratic**:
Since the quadratic \( x^2 - 5x + 7 \) does not have real roots and opens upwards (as the coefficient of \( x^2 \) is positive), it is always positive for all real \( x \).

4. **Analyze the inequality**:
Since \( x^2 - 5x + 7 > 0 \) for all \( x \), the entire expression \( 3x(x^2 - 5x + 7) \) changes sign based solely on \( 3x \):
\[
3x(x^2 - 5x + 7) < 0 \implies 3x < 0 \implies x < 0
\]

5. **Conclusion**:
Thus, the solution to the inequality \( 3x(x^2 - 5x + 7) < 0 \) is:
\[
x < 0
\]

This means the inequality holds for all negative values of \( x \).