Answer:
x = 6 or x = 3 or x = -3
Explanation:
Solve for x over the real numbers:
x^3 - 6 x^2 - 9 x + 54 = 0
Hint: | Factor the left hand side.
The left hand side factors into a product with three terms:
(x - 6) (x - 3) (x + 3) = 0
Hint: | Find the roots of each term in the product separately.
Split into three equations:
x - 6 = 0 or x - 3 = 0 or x + 3 = 0
Hint: | Look at the first equation: Solve for x.
Add 6 to both sides:
x = 6 or x - 3 = 0 or x + 3 = 0
Hint: | Look at the second equation: Solve for x.
Add 3 to both sides:
x = 6 or x = 3 or x + 3 = 0
Hint: | Look at the third equation: Solve for x.
Subtract 3 from both sides:
Answer: x = 6 or x = 3 or x = -3