2x²+6x=0

To solve the equation \( 2x^2 + 6x = 0 \), we can factor out the common term.

1. Start by factoring out the greatest common factor, which is \( 2x \):

\[ 2x(x + 3) = 0 \]

2. Set each factor equal to zero:

\[ 2x = 0 \quad \text{or} \quad x + 3 = 0 \]

From \( 2x = 0 \):

\[ x = 0 \]

From \( x + 3 = 0 \):

\[ x = -3 \]

3. Therefore, the solutions to the equation \( 2x^2 + 6x = 0 \) are:

\[ x = 0 \quad \text{and} \quad x = -3 \]