\{ q ( 2 A + B ) - B = 2 \}
Solve for q, A, B
q=\frac{B+2}{2A+B}\text{, }A\neq -\frac{B}{2}\text{, }B\in \mathrm{R}
q\in \mathrm{R}\text{, }A=1\text{, }B=-2
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