Which of the following is a complete set of solutions to 3x3+9x2−54x=0?(1 point)

Question

Responses

0
0

no solutions
no solutions

0, −3, 6
0, negative 3 , 6

0, 3, −6
0, 3, negative 6

Answer 1

To solve the equation \(3x^3 + 9x^2 - 54x = 0\), we start by factoring out the common term.

1. Factor out \(3x\): \[ 3x(x^2 + 3x - 18) = 0 \]

2. This gives us one solution: \[ 3x = 0 \implies x = 0 \]

3. Now, we need to solve the quadratic equation \(x^2 + 3x - 18 = 0\). We can either factor it or use the quadratic formula.

4. Attempting to factor: \[ x^2 + 3x - 18 = (x + 6)(x - 3) \] This gives us: \[ x + 6 = 0 \implies x = -6 \] and \[ x - 3 = 0 \implies x = 3 \]

5. Thus, the complete set of solutions is: \[ x = 0, x = 3, x = -6 \]

Therefore, the correct answer is: \[ \boxed{0, 3, -6} \]