To solve the equation
notice that the expression on the left-hand side is the difference of two cubes. We can use that to rewrite it as a product.
The tells us that we can solve the equation by setting each of the factors equal to
and solving the resulting equations separately.
Let's find the solution to the first equation.
The second equation we will solve using the .
We should simplify these expressions, if possible. The becomes
and the can be simplified.
After we have simplified, we the complex solutions to the quadratic equation can be written as