2x^2+5x=0

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

1. Factor out \( x \): \[ x(2x + 5) = 0 \]

2. Set each factor equal to zero: \[ x = 0 \quad \text{or} \quad 2x + 5 = 0 \]

3. Solve the second equation for \( x \): \[ 2x + 5 = 0 \implies 2x = -5 \implies x = -\frac{5}{2} \]

So the solutions to the equation \( 2x^2 + 5x = 0 \) are: \[ x = 0 \quad \text{and} \quad x = -\frac{5}{2} \]