Solve the equation.
\[
4 x^{3}-15 x^{2}-4 x=0
\]

Answer

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Answer

Final Answer: The solutions to the equation are \(\boxed{-\frac{1}{4}, 0, 4}\).

Steps

Step 1 ：Given the equation \(4x^{3}-15x^{2}-4x=0\).

Step 2 ：First, factor out the common factor, which is x in this case. This gives us \(x(4x^{2}-15x-4)=0\).

Step 3 ：Then, factor the quadratic equation \(4x^{2}-15x-4\) to get \(x(x - 4)(4x + 1)=0\).

Step 4 ：Setting each factor equal to zero gives the solutions \(-\frac{1}{4}, 0, 4\).

Step 5 ：Final Answer: The solutions to the equation are \(\boxed{-\frac{1}{4}, 0, 4}\).