Find the roots of the following curve: y = 6x^2 - 4x.

The two terms in the quadratic equation share the factors 2 and x, so these can be brought outside the bracket as shown: y = 2x(3x-2). In order to solve for the roots (where the curve intercepts the x-axis), we must set y = 0 and hence satisfy the equation: 2x(3x-2) = 0. We can see that there are two possible solutions: 2x = 0 AND 3x-2 = 0. The first equation gives x = 0 and as for the second we can solve by adding 2 to both sides and then dividing by 3: 3x-2=0, 3x = 2, x = 2/3. So we have calculated the roots to be: x = 0 AND x = 2/3.