Solve 3ab+s=a^2b

$$3 a b + s = a ^ { 2 } b$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{s}{a\left(3-a\right)}\text{, }&a\neq 3\text{ and }a\neq 0\\b\in \mathrm{C}\text{, }&\left(a=0\text{ or }a=3\right)\text{ and }s=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract a^{2}b from both sides.

$$3ab+s-a^{2}b=0$$

Subtract s from both sides. Anything subtracted from zero gives its negation.

$$3ab-a^{2}b=-s$$

Combine all terms containing b.

$$\left(3a-a^{2}\right)b=-s$$

Divide both sides by 3a-a^{2}.

$$\frac{\left(3a-a^{2}\right)b}{3a-a^{2}}=-\frac{s}{3a-a^{2}}$$

Dividing by 3a-a^{2} undoes the multiplication by 3a-a^{2}.

$$b=-\frac{s}{3a-a^{2}}$$

Divide -s by 3a-a^{2}.

$$b=-\frac{s}{a\left(3-a\right)}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{s}{a\left(3-a\right)}\text{, }&a\neq 3\text{ and }a\neq 0\\b\in \mathrm{R}\text{, }&\left(a=0\text{ or }a=3\right)\text{ and }s=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract a^{2}b from both sides.

$$3ab+s-a^{2}b=0$$

Subtract s from both sides. Anything subtracted from zero gives its negation.

$$3ab-a^{2}b=-s$$

Combine all terms containing b.

$$\left(3a-a^{2}\right)b=-s$$

Divide both sides by 3a-a^{2}.

$$\frac{\left(3a-a^{2}\right)b}{3a-a^{2}}=-\frac{s}{3a-a^{2}}$$

Dividing by 3a-a^{2} undoes the multiplication by 3a-a^{2}.

$$b=-\frac{s}{3a-a^{2}}$$

Divide -s by 3a-a^{2}.

$$b=-\frac{s}{a\left(3-a\right)}$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{\sqrt{b\left(4s+9b\right)}-3b}{2b}\text{; }a=\frac{\sqrt{b\left(4s+9b\right)}+3b}{2b}\text{, }&b\neq 0\\a\in \mathrm{C}\text{, }&b=0\text{ and }s=0\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{\sqrt{b\left(4s+9b\right)}-3b}{2b}\text{; }a=\frac{\sqrt{b\left(4s+9b\right)}+3b}{2b}\text{, }&\left(s\neq 0\text{ and }b=-\frac{4s}{9}\right)\text{ or }\left(b\leq -\frac{4s}{9}\text{ and }b<0\right)\text{ or }\left(b\geq -\frac{4s}{9}\text{ and }b>0\right)\\a\in \mathrm{R}\text{, }&b=0\text{ and }s=0\end{matrix}\right.$$