To solve the equation x³ - x² = 4x² - 8x + 4, we can start by rearranging the terms to get all terms on one side of the equation:

x³ - x² - 4x² + 8x - 4 = 0

Combining like terms, we have:

x³ - 5x² + 8x - 4 = 0

Next, we can try to factor the equation. We can start by looking for any common factors among the terms. In this case, there is no common factor among all the terms.

So, we can try to factor by grouping. We group the terms in pairs:

(x³ - 5x²) + (8x - 4) = 0

Now, we can factor out the greatest common factor from each pair:

x²(x - 5) + 4(2x - 1) = 0

Now, we can factor out the common factors:

x²(x - 5) + 4(2x - 1) = 0

(x² + 4)(x - 5) = 0

Now, we can set each factor equal to zero and solve for x:

x² + 4 = 0 or x - 5 = 0

For the first equation, x² + 4 = 0, there are no real solutions since the square of any real number is always positive or zero.

For the second equation, x - 5 = 0, we can solve for x:

x = 5

Therefore, the solution to the equation x³ - x² = 4x² - 8x + 4 is x = 5.