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Can anyone please help me work out how to find these unknowns?

Basically I'm doing some beam analysis, I've done the engineering bit, now its the maths I've come stuck with.

I have created six equation and have six unknowns, equation 1 works out C1 to equal zero, so there are five more unknowns to find.

Not sure how to use simultaneous method or if I can just transpose. So the five remaining unknowns to find are C2,M,q1,q2,q3

Can anyone please show me how to do this it would be much appreciated.

Thanks

hmk999