Hi Amanda,
The goal to solving an equation such as this algebraically is to first factor it:
x³ - 4x² + 4x = 0 - remove the GCF of x first
x(x² - 4x + 4) = 0 - now factor the quadratic in the brackets
x(x - 2)(x - 2) = 0

Now set each factor to zero and solve for x:

x = 0 x - 2 = 0 (this factor occurs twice, but only solve it once)
x = 2

Therefore the solutions to this equation are 0, and 2 (a solution that occurs twice)

Hope this helps,
Leeanne