\(\left(x^2+x\right)^2+4\left(x^2+x\right)-12\)
\(=\left(x^2+x\right)\left(x^2+x+4\right)-12\)
\(=\left(x^2+x+2-2\right)\left(x^2+x+2+2\right)-12\)
\(=\left(x^2+x+2\right)-2^2-12\)
\(=\left(x^2+x+2\right)-16\)
\(=\left(x^2+x+2\right)-4^2\)
\(=\left(x^2+x+4\right)\left(x^2+x-4\right)\)