Solve bc=ab+a^2+ac

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

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Subtract ab from both sides.

$$bc-ab=a^{2}+ac$$

Combine all terms containing b.

$$\left(c-a\right)b=a^{2}+ac$$

Divide both sides by c-a.

$$\frac{\left(c-a\right)b}{c-a}=\frac{a\left(a+c\right)}{c-a}$$

Dividing by c-a undoes the multiplication by c-a.

$$b=\frac{a\left(a+c\right)}{c-a}$$

Solve for b

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

Steps for Solving Linear Equation

Subtract ab from both sides.

$$bc-ab=a^{2}+ac$$

Combine all terms containing b.

$$\left(c-a\right)b=a^{2}+ac$$

Divide both sides by c-a.

$$\frac{\left(c-a\right)b}{c-a}=\frac{a\left(a+c\right)}{c-a}$$

Dividing by c-a undoes the multiplication by c-a.

$$b=\frac{a\left(a+c\right)}{c-a}$$

Solve for a (complex solution)

$$a=\frac{-\sqrt{b^{2}+6bc+c^{2}}-b-c}{2}$$

$$a=\frac{\sqrt{b^{2}+6bc+c^{2}}-b-c}{2}$$

Solve for a

$$a=\frac{-\sqrt{b^{2}+6bc+c^{2}}-b-c}{2}$$

$$a=\frac{\sqrt{b^{2}+6bc+c^{2}}-b-c}{2}\text{, }b\leq -2\sqrt{2}|c|-3c\text{ or }b\geq 2\sqrt{2}|c|-3c$$