Show that $\frac 1{4\pi |x|} e^{-c|x|}$ is a fundamental solution for $-\Delta+c^2$ on $\mathbb R^3$

Question

[Introduction to Partial Differential Equations - Gerald B. Folland, chapter 2, section C, question 6]

Show that $$\frac 1{4\pi |r|} e^{-c|r|}$$ is a fundamental solution for $$-\Delta+c^2\qquad (c\in \mathbb C)$$ on $\mathbb R^3$.

I have been able to show that it is indeed a solution, i.e., $$\Delta F = c^2F$$ But, I can't figure out how to show that it is a fundamental solution. Please help me in that.

Also, the way I proved that it is a solution, it took me pages of hardwork - will it be possible to simplify the calculations somehow?

Note that I know what a Fundamental Solution is. I just don't see any way to complete the required calculation in finite amount of time :)

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Note that here $r=\sqrt{x^2+y^2+z^2}$.