How to solve for g 10g^2+33g=9-2g^2

Given:  10g^2+33g=9-2g^2

Group the q^2 terms first, then the q terms, and finally the constants:

12g^2 + 33q - 9 = 0.  Make sure you agree with this, or otherwise fix it.

Tools for solving quadratic equations include the following and more:

graphing
quadratic formula
completing the square

I've graphed this simplified quadratic on my TI-83 calculator and see that -3 seems to be a root.  Let's check it!
     
-3  /   12    33    -9
                 -36    9
     
        12      -3      0           Since the remainder is zero, -3 is a root and (x+3) is                                          a factor.  The other factors are 3 and (4x -1)

Then 3(4g-1)(g+3) = 0, with the result that g = 1/4 and g = -3.

Please check these roots by subst. into the original equation.