Solve aq-bq^2-q^2=0

$$a q - b q ^ { 2 } - q ^ { 2 } = 0$$

Solve for a

$$\left\{\begin{matrix}\\a=q\left(b+1\right)\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&q=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add q^{2} to both sides. Anything plus zero gives itself.

$$aq-bq^{2}=q^{2}$$

Add bq^{2} to both sides.

$$aq=q^{2}+bq^{2}$$

The equation is in standard form.

$$qa=bq^{2}+q^{2}$$

Divide both sides by q.

$$\frac{qa}{q}=\frac{\left(b+1\right)q^{2}}{q}$$

Dividing by q undoes the multiplication by q.

$$a=\frac{\left(b+1\right)q^{2}}{q}$$

Divide \left(1+b\right)q^{2} by q.

$$a=bq+q$$

Solve for b

$$\left\{\begin{matrix}b=\frac{a}{q}-1\text{, }&q\neq 0\\b\in \mathrm{R}\text{, }&q=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add q^{2} to both sides. Anything plus zero gives itself.

$$aq-bq^{2}=q^{2}$$

Subtract aq from both sides.

$$-bq^{2}=q^{2}-aq$$

The equation is in standard form.

$$\left(-q^{2}\right)b=q^{2}-aq$$

Divide both sides by -q^{2}.

$$\frac{\left(-q^{2}\right)b}{-q^{2}}=\frac{q\left(q-a\right)}{-q^{2}}$$

Dividing by -q^{2} undoes the multiplication by -q^{2}.

$$b=\frac{q\left(q-a\right)}{-q^{2}}$$

Divide q\left(q-a\right) by -q^{2}.

$$b=\frac{a}{q}-1$$