2x+8x^2=0

To solve the equation \(2x + 8x^2 = 0\), we can start by factoring out the common terms.

1. Factor out the common term: \[ 2x(1 + 4x) = 0 \]

2. Set each factor to zero:

   • From \(2x = 0\), we find: \[ x = 0 \]

   • From \(1 + 4x = 0\), we solve for \(x\): \[ 4x = -1 \implies x = -\frac{1}{4} \]

3. List the solutions: The solutions to the equation \(2x + 8x^2 = 0\) are: \[ x = 0 \quad \text{and} \quad x = -\frac{1}{4} \]