Solve for r
r=q^{2}\left(q^{2}+q-1\right)
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r-q^{3}+1-q^{4}=1-q^{2}
Swap sides so that all variable terms are on the left hand side.
r+1-q^{4}=1-q^{2}+q^{3}
Add q^{3} to both sides.
r-q^{4}=1-q^{2}+q^{3}-1
Subtract 1 from both sides.
r-q^{4}=-q^{2}+q^{3}
Subtract 1 from 1 to get 0.
r=-q^{2}+q^{3}+q^{4}
Add q^{4} to both sides.
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