Solve x=ab^2+bc

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

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{bc-x}{b^{2}}\text{, }&b\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ab^{2}+bc=x$$

Subtract bc from both sides.

$$ab^{2}=x-bc$$

The equation is in standard form.

$$b^{2}a=x-bc$$

Divide both sides by b^{2}.

$$\frac{b^{2}a}{b^{2}}=\frac{x-bc}{b^{2}}$$

Dividing by b^{2} undoes the multiplication by b^{2}.

$$a=\frac{x-bc}{b^{2}}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{bc-x}{b^{2}}\text{, }&b\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ab^{2}+bc=x$$

Subtract bc from both sides.

$$ab^{2}=x-bc$$

The equation is in standard form.

$$b^{2}a=x-bc$$

Divide both sides by b^{2}.

$$\frac{b^{2}a}{b^{2}}=\frac{x-bc}{b^{2}}$$

Dividing by b^{2} undoes the multiplication by b^{2}.

$$a=\frac{x-bc}{b^{2}}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{\sqrt{4ax+c^{2}}+c}{2a}\text{; }b=-\frac{-\sqrt{4ax+c^{2}}+c}{2a}\text{, }&a\neq 0\\b=\frac{x}{c}\text{, }&a=0\text{ and }c\neq 0\\b\in \mathrm{C}\text{, }&a=0\text{ and }c=0\text{ and }x=0\end{matrix}\right.$$

Solve for b

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