(Calc I problem) Can someone help me understand the solution to this problem? I don't understand how they get a = 2/3 and c=4/9 at the end??
Link to solution: http://www.marywood.edu/math/challenge/problems/pow20100228sol.pdf

Question

anonymous · Answer

*at the end

anonymous · Answer

do you know how they get the a? because they got the c by plugging in a: f(a)=c

anonymous · Answer

c = f(a)  plug in a and solve for c

anonymous · Answer

c=2(2/3)-3(2/3)^3 = 4/3 - 8/9 = 12/9 - 8/9 = 4/9

anonymous · Answer

Oh okay, I understand for c but how did they simplify the equation to get a?

anonymous · Answer

they substituted in for c.  c = 2a - 3a^3,  so now after they integrated, a is the only variable and they solved for it.

anonymous · Answer

No, I mean what is going on with 1-3/4a^2 =2-3a^2?

anonymous · Answer

they factored out a^2 from both sides

anonymous · Answer

Wow, how was I confused by that?!! Thank you!

anonymous · Answer

no worries!