I have an equation sqrt(x+1)+sqrt(x+2)+2*sqrt((x+1)*(x+2))+2*x-3=0. Now I want to introduce new variable t = t=sqrt(x+1)+sqrt(x+2). How must I do?

I did

**f:=x->sqrt(x+1)+sqrt(x+2)+2*sqrt((x+1)*(x+2))+2*x-3:**

**sol:=solve(t=sqrt(x+1)+sqrt(x+2),x):**

**A:=f(sol):**

**simplify(A);**

But I did not receive a good answer. Please help me.