Final answer:
To solve the equation, we first group the terms and then factor out the common factors. After setting each factor equal to zero, we find the solutions to be x = ±√6, x = 0, and x = 1.
Step-by-step explanation:
We can solve the equation by factoring.
First, we group the terms:
x²(x² - x) + 2(x² - x) - 8 = 0
Now, we notice that each group of terms has a common factor of (x² - x), so we can factor it out:
(x² + 2 - 8)(x² - x) = 0
Simplifying further, we get:
(x² - 6)(x² - x) = 0
Now, we can set each factor equal to zero and solve for x:
x² - 6 = 0 or x² - x = 0
Solving the first equation, we get:
x = ±√6
For the second equation, we can factor out x:
x(x - 1) = 0
So, x = 0 or x = 1
Therefore, the solutions to the equation are:
x = ±√6, x = 0, x = 1