To solve the equation 8x^2 - 4x = 0, we can factor out the common factor of 4x:

4x(2x - 1) = 0

Now, we can set each factor equal to zero and solve for x:

4x = 0 or 2x - 1 = 0

For the first equation, dividing both sides by 4 gives:

x = 0

For the second equation, adding 1 to both sides and then dividing by 2 gives:

2x = 1
x = 1/2

Therefore, the solutions to the equation 8x^2 - 4x = 0 are x = 0 and x = 1/2.