Solve ab+a+ab^2=a

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

Solve for a

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

Steps for Solving Linear Equation

Subtract a from both sides.

$$ab+a+ab^{2}-a=0$$

Combine a and -a to get 0.

$$ab+ab^{2}=0$$

Combine all terms containing a.

$$\left(b+b^{2}\right)a=0$$

The equation is in standard form.

$$\left(b^{2}+b\right)a=0$$

Divide 0 by b+b^{2}.

$$a=0$$

Solve for b

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