Is it possible to factor a quadratic equation when $a$, $b$, and $c$ are all equal? I have the equation $4x^2+4x+4$ to factor. I know that need to start with
$$(2x \quad )(2x \quad )$$
to make $4^2$, but I can't seem to factor the rest of the way. What should I do?

We have $$4x^2+4x+4=4(x^2+x+1)$$  Let's consider $$f(x)=x^2+x+1$$ $$x=\frac{-1\pm\sqrt{1^2-4(1)(1)}}{2}=\frac{-1\pm i\sqrt3}{2}$$ Thus we have $$4x^2+4x+4=4\left(x-\frac{-1+i\sqrt3}{2}\right)\left(x-\frac{-1-i\sqrt3}{2}\right)$$ $$=4\left(x+\frac{1-i\sqrt3}{2}\right)\left(x+\frac{1+i\sqrt3}{2}\right)$$ $$=\left(2x+1-i\sqrt3\right)\left(2x+1+i\sqrt3\right)$$
