Question 250296
-9x^2+4y^2+36x+24y-36=0

Do you start off as -9x^2+4y^2+36x+24y=-36
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That's a good step 1.
Group the x and y terms:
-9x^2+36x + 4y^2+24y = -36
-(9x^2-36x) + 4y^2+24y = -36
Add coeffs to complete the squares:
-(9x^2-36x+36) + (4y^2+24y+36) = -36 - 36 + 36
-(3x-6)^2 + (2y+6)^2 = -36
(2y+6)^2 - (3x-6)^2 = 36