Solve q=a^3b:a.b

$$q = a ^ { 3 } b : a . b$$

Solve for b

$$b=\frac{q}{a^{2}}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

$$qa=a^{3}b$$

Swap sides so that all variable terms are on the left hand side.

$$a^{3}b=qa$$

The equation is in standard form.

$$a^{3}b=aq$$

Divide both sides by a^{3}.

$$\frac{a^{3}b}{a^{3}}=\frac{aq}{a^{3}}$$

Dividing by a^{3} undoes the multiplication by a^{3}.

$$b=\frac{aq}{a^{3}}$$

Divide qa by a^{3}.

$$b=\frac{q}{a^{2}}$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-b^{-\frac{1}{2}}\sqrt{q}\text{; }a=b^{-\frac{1}{2}}\sqrt{q}\text{, }&b\neq 0\text{ and }q\neq 0\\a\neq 0\text{, }&q=0\text{ and }b=0\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}a=\sqrt{\frac{q}{b}}\text{; }a=-\sqrt{\frac{q}{b}}\text{, }&\left(b<0\text{ and }q<0\right)\text{ or }\left(b>0\text{ and }q>0\right)\\a\neq 0\text{, }&q=0\text{ and }b=0\end{matrix}\right.$$