Question

How do you solve `x (x^2 + 2x + 3)=4`?

Answer 1

Distribute: `x^3+2x^2+3x=4`

Rearrange: `x^3+2x^2+3x-4=0`

It would be great if we could now factor the left-hand side. Unfortunately, the roots of this are an irrational real number as well as two complex numbers with irrational real and imaginary parts.

Using a computer or calculator gives approximate roots:

`x\approx 0.776045`, `x\approx -1.38802\pm 1.79659i`

There is a method/formula for finding exact expressions for these roots (involving roots that are irrational), but it's not pleasant:
general method/formula for cubic roots on Wikipedia