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: \[ x = 0 \quad \text{and} \quad x = -\frac{1}{4} \]