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-y^{2}-6y+y^{2}=9
Add y^{2} to both sides.
-6y=9
Combine -y^{2} and y^{2} to get 0.
y=\frac{9}{-6}
Divide both sides by -6.
y=-\frac{3}{2}
Reduce the fraction \frac{9}{-6} to lowest terms by extracting and canceling out 3.