10x²+5x=0

To solve the equation \(10x^2 + 5x = 0\), you can factor out the common term:

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

2. Set each factor equal to zero: \[ 5x = 0 \quad \text{or} \quad 2x + 1 = 0 \]

3. Solve for \(x\):

   • For the first equation: \[ 5x = 0 \implies x = 0 \]

   • For the second equation: \[ 2x + 1 = 0 \implies 2x = -1 \implies x = -\frac{1}{2} \]

Thus, the solutions to the equation \(10x^2 + 5x = 0\) are: \[ x = 0 \quad \text{and} \quad x = -\frac{1}{2} \]