Solve the following equation: x^3 + 8x^2 + 4x - 48=0

To solve a cubic equation, you first have to guess at values for x that will solve the equation. Generally, it is good practice to start with 0, then use +/- 1, +/- 2 and so on until you find a value that works. For this particular question, the value x = 2 works to solve the equation. Following this, we factorise the solution out of the equation. i.e. as x - 2 = 0 for x = 2, we factorise (x - 2) out of our cubic equation. This gives us the following: (x-2)(x^2 + 10x + 24) = 0. We can then solve the quadratic equation that makes up the second term to find the remaining two solutions for the cubic equation. Using the quadratic formula to do so quickly, we find the remaining two solutions are x = -4 and x = -6. In summary, our three solutions are x = 2, -4 and -6.