5х²+ 9х =0;

To solve the equation \(5x^2 + 9x = 0\), we can factor out the common term \(x\):

\[ x(5x + 9) = 0 \]

Setting each factor equal to zero gives us two possible solutions:

1. \(x = 0\)
2. \(5x + 9 = 0\)

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

\[ 5x + 9 = 0 \implies 5x = -9 \implies x = -\frac{9}{5} \]

Therefore, the solutions to the equation \(5x^2 + 9x = 0\) are:

\[ x = 0 \quad \text{and} \quad x = -\frac{9}{5} \]