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 $- \frac{1}{4}, 0, 4$ .

Steps

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

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

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

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 $- \frac{1}{4}, 0, 4$ .