Find the roots of the equation `3x^(2)+2x=0`

Answer

To find the roots of the equation \(3x^2 + 2x = 0\), we can follow these steps:

### Step 1: Factor the equation
We start with the equation:
\[ 3x^2 + 2x = 0 \]
We can factor out \(x\) from both terms:
\[ x(3x + 2) = 0 \]

### Step 2: Set each factor to zero
Now, we set each factor equal to zero:
1. \(x = 0\)
2. \(3x + 2 = 0\)

### Step 3: Solve for \(x\) in the second equation
Now, we solve the second equation:
\[ 3x + 2 = 0 \]
Subtract \(2\) from both sides:
\[ 3x = -2 \]
Now, divide by \(3\):
\[ x = -\frac{2}{3} \]

### Conclusion
The roots of the equation \(3x^2 + 2x = 0\) are:
\[ x = 0 \quad \text{and} \quad x = -\frac{2}{3} \]

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