x(5+x)=0

To solve the equation \( x(5+x) = 0 \), we can use the zero product property, which states that if a product of factors equals zero, at least one of the factors must be zero.

Setting each factor equal to zero:

1. \( x = 0 \)
2. \( 5 + x = 0 \)

For the second equation, we can solve for \( x \):

\[ 5 + x = 0 \\ x = -5 \]

So the solutions to the equation \( x(5+x) = 0 \) are:

\[ x = 0 \quad \text{and} \quad x = -5 \]