Solve a^2+3c^2+5bc=36

$$a ^ { 2 } + 3 c ^ { 2 } + 5 b c = 36$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{a^{2}+3c^{2}-36}{5c}\text{, }&c\neq 0\\b\in \mathrm{C}\text{, }&\left(a=6\text{ or }a=-6\right)\text{ and }c=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract a^{2} from both sides.

$$3c^{2}+5bc=36-a^{2}$$

Subtract 3c^{2} from both sides.

$$5bc=36-a^{2}-3c^{2}$$

The equation is in standard form.

$$5cb=36-3c^{2}-a^{2}$$

Divide both sides by 5c.

$$\frac{5cb}{5c}=\frac{36-3c^{2}-a^{2}}{5c}$$

Dividing by 5c undoes the multiplication by 5c.

$$b=\frac{36-3c^{2}-a^{2}}{5c}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{a^{2}+3c^{2}-36}{5c}\text{, }&c\neq 0\\b\in \mathrm{R}\text{, }&c=0\text{ and }|a|=6\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract a^{2} from both sides.

$$3c^{2}+5bc=36-a^{2}$$

Subtract 3c^{2} from both sides.

$$5bc=36-a^{2}-3c^{2}$$

The equation is in standard form.

$$5cb=36-3c^{2}-a^{2}$$

Divide both sides by 5c.

$$\frac{5cb}{5c}=\frac{36-3c^{2}-a^{2}}{5c}$$

Dividing by 5c undoes the multiplication by 5c.

$$b=\frac{36-3c^{2}-a^{2}}{5c}$$

Solve for a (complex solution)

$$a=-\sqrt{36-3c^{2}-5bc}$$

$$a=\sqrt{36-3c^{2}-5bc}$$

Solve for a

$$a=\sqrt{36-3c^{2}-5bc}$$

$$a=-\sqrt{36-3c^{2}-5bc}\text{, }c\geq \frac{-\sqrt{25b^{2}+432}-5b}{6}\text{ and }c\leq \frac{\sqrt{25b^{2}+432}-5b}{6}$$