Use the distributive property to multiply $4$ by $2x+1$.
$$4x^{2}-8x+4=\left(8x+4\right)\left(x+1\right)$$
Apply the distributive property by multiplying each term of $8x+4$ by each term of $x+1$.
$$4x^{2}-8x+4=8x^{2}+8x+4x+4$$
Combine $8x$ and $4x$ to get $12x$.
$$4x^{2}-8x+4=8x^{2}+12x+4$$
Subtract $8x^{2}$ from both sides.
$$4x^{2}-8x+4-8x^{2}=12x+4$$
Combine $4x^{2}$ and $-8x^{2}$ to get $-4x^{2}$.
$$-4x^{2}-8x+4=12x+4$$
Subtract $12x$ from both sides.
$$-4x^{2}-8x+4-12x=4$$
Combine $-8x$ and $-12x$ to get $-20x$.
$$-4x^{2}-20x+4=4$$
Subtract $4$ from both sides.
$$-4x^{2}-20x+4-4=0$$
Subtract $4$ from $4$ to get $0$.
$$-4x^{2}-20x=0$$
Factor out $x$.
$$x\left(-4x-20\right)=0$$
To find equation solutions, solve $x=0$ and $-4x-20=0$.
$$x=0$$ $$x=-5$$
Substitute $-5$ for $x$ in the equation $\sqrt{x+4}-\sqrt{x+1}=\sqrt{2x+1}$. The expression $\sqrt{-5+4}$ is undefined because the radicand cannot be negative.
