*Can you*find all the roots?,' but I know this will get solved.

This problem was posted a few years ago in the math department of the college I attended. I got a math club t-shirt and a certificate for getting the correct answer.

Find all the roots of the following equation without the use of technology.:

x

^{6}sin(x)+240-14x

^{5}sin(x)-308x+69x

^{4}sin(x)+22x

^{2}-126x

^{3}sin(x)+126x

^{3}-22x

^{2}sin(x)-69x

^{4}+308xsin(x)+14x

^{5}-240sin(x)-x

^{6}=0