Answer:
x = 6 or x = 0 or x = -8
Explanation:
Solve for x over the real numbers:
2 x^3 - 4 x^2 - 96 x = -8 x^2
Add 8 x^2 to both sides:
2 x^3 + 4 x^2 - 96 x = 0
The left-hand side factors into a product with four terms:
2 x (x - 6) (x + 8) = 0
Divide both sides by 2:
x (x - 6) (x + 8) = 0
Split into three equations:
x - 6 = 0 or x = 0 or x + 8 = 0
Add 6 to both sides:
x = 6 or x = 0 or x + 8 = 0
Subtract 8 from both sides:
Answer: x = 6 or x = 0 or x = -8