To solve this equation, we can factor out a common factor of 4:

4(3x^4 - 3x^3 + 4x^2 - 4x + 4) = 0

Now we have:

3x^4 - 3x^3 + 4x^2 - 4x + 4 = 0

Next, we can try to factor this polynomial by grouping:

3x^4 - 3x^3 + 4x^2 - 4x + 4
= 3x^3(x - 1) + 4x^2(x - 1) + 4
= (3x^3 + 4x^2)(x - 1) + 4
= x^2(3x + 4)(x - 1) + 4

Therefore, the solutions to the equation are x = 1, -4/3.