find all real and imaginary solutions of f(x) = x^3 + x^2 + 13x -15
You should be able to see that $\displaystyle f(1) = 1^3 + 1^2 + 13(1) - 15 = 0$.
So by the remainder and factor theorems, that means $\displaystyle x - 1$ is a factor.
By using long division:
$\displaystyle x^3 + x^2 + 13x - 15 = (x - 1)(x^2 + 2x + 15)$.
Now use the Quadratic Formula on the Quadratic factor to find the imaginary solutions.