since the equation is equal to 0 you are looking for the x roots.
-2x^2 + x = 0
x(-2x + 1) = 0
so x = 0 or -2x+1 = 0
1 = 2x
1/2 = x
CHECK:
-2x^2 + x = 0
substitute in 0 for x
-2*0 + 0 = 0
0=0 check it works
-2x^2 + x = 0
substitute in 1/2 for x
-2(1/2^2) + 1/2 = 0
-2*1/4 + 1/2 = 0
-1/2 + 1/2 = 0
0=0 check it works
the solution set is {1/2, 0}