I need to solve this equation $$(x^2-4x+4)(x^2+6x+9)=2x^2+2x+12$$
If I simplify I'll get $4$th degree.
Is there any simple method to factorize and solve?
I can see that: $$(x-2)^2\cdot(x+3)^2=2(x^2+x+6)$$
I'm not allowed to use polynomial division.
Wolfram said that it's equal to: $$(x^2+x-6)^2=2(x^2+x+6)$$ and then it's easy because I can put $t=x^2+x$ but I don't know how to get this factorization.