Find a nonzero solution to the equation $\sqrt{4c-5c^2} = 0$.
I need to find a value of $c$ that makes the expression under the square root equal to zero, since that's the only way a square root can be zero. So I set $4c-5c^2 = 0$ and try to solve for $c$. I can factor out a $c$ from both terms and get $c(4-5c) = 0$. Now I have a product of two factors equal to zero, so either one of them must be zero. That means $c = 0$ or $4-5c = 0$. But $c = 0$ is not a nonzero solution, so I can ignore that. To solve for $c$ in $4-5c = 0$, I can add $5c$ to both sides and get $4 = 5c$. Then I can divide both sides by $5$ and get $c = \frac{4}{5}$. This is a nonzero solution to the equation, and I can check that it works by plugging it back into the original equation and seeing that it satisfies it. 