Please help solving the equation $(2x+1)^2-3(x+1)^2=0$

Question

I am doing exercises to practice for finals. Please help solve the equation $$(2x+1)^2-3(x+1)^2=0$$

I tried solving it but I got to $x^2-2x-2=0$ and I got stuck there.

Thanks in advance.

Answer 1

It is a quadratic equation, that is, an equation of the form $ax^2+bx+c=0$. Use the general formula: $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ There may be 0, 1 or 2 solutions (depending on the sign of $b^2-4ac$).

Answer 2

$x^2-2x-2=0\implies (x-1)^2-3=0$.

Can you take it from here?