STRATEGY: As with all GRE Multiple Choice questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
In fact, I can immediately see that x = 0 is a solution, since both sides of the equation would evaluate to be 0.
Let's go with that approach

When we plug x = 0 into the equation, we get: 0³ = 3(0)² − 2(0), which simplifies to be: 0 = 0. WORKS!
Since x = 0 is a solution to the given equation, we can eliminate answers choices A, B and E, since they don't list x = 0 as a possible solution.

This leaves us with answer choices C and D.
Both answer choices say that x = 1, which means x = 1 must be a solution. So we won't bother testing that value.
However, choice C says x = 2 is a solution, and choice D says x = 2 isn't a solution, so let's test x = 2

We get: 2³ = 3(2)² − 2(2), which simplifies to be: 8 = 8. WORKS!
Since x = 2 is a solution to the given equation, we can eliminate answer choices D

Answer: C

ALGEBRAIC APPROACH
Given: x³ = 3x² − 2x
Rearrange terms to get: x³ - 3x² + 2x = 0
Factor out x to get: x(x² - 3x + 2) = 0
Factor the expression in the parentheses to get: x(x - 1)(x - 2) = 0
At this point, we can see that the solutions are x = 0, x = 1 and x = 2

Answer: C