Solve 136a^2-4b^2=(6a+2b)Cb

$$136 a ^ { 2 } - 4 b ^ { 2 } = ( 6 a + 2 b ) C b$$

Solve for C (complex solution)

$$\left\{\begin{matrix}C=-\frac{2\left(b^{2}-34a^{2}\right)}{b\left(3a+b\right)}\text{, }&b\neq 0\text{ and }a\neq -\frac{b}{3}\\C\in \mathrm{C}\text{, }&a=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6a+2b by C.

$$136a^{2}-4b^{2}=\left(6aC+2bC\right)b$$

Use the distributive property to multiply 6aC+2bC by b.

$$136a^{2}-4b^{2}=6aCb+2Cb^{2}$$

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

$$6aCb+2Cb^{2}=136a^{2}-4b^{2}$$

Combine all terms containing C.

$$\left(6ab+2b^{2}\right)C=136a^{2}-4b^{2}$$

Divide both sides by 6ab+2b^{2}.

$$\frac{\left(6ab+2b^{2}\right)C}{6ab+2b^{2}}=\frac{136a^{2}-4b^{2}}{6ab+2b^{2}}$$

Dividing by 6ab+2b^{2} undoes the multiplication by 6ab+2b^{2}.

$$C=\frac{136a^{2}-4b^{2}}{6ab+2b^{2}}$$

Divide 136a^{2}-4b^{2} by 6ab+2b^{2}.

$$C=\frac{2\left(34a^{2}-b^{2}\right)}{b\left(3a+b\right)}$$

Solve for C

$$\left\{\begin{matrix}C=-\frac{2\left(b^{2}-34a^{2}\right)}{b\left(3a+b\right)}\text{, }&b\neq 0\text{ and }a\neq -\frac{b}{3}\\C\in \mathrm{R}\text{, }&a=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6a+2b by C.

$$136a^{2}-4b^{2}=\left(6aC+2bC\right)b$$

Use the distributive property to multiply 6aC+2bC by b.

$$136a^{2}-4b^{2}=6aCb+2Cb^{2}$$

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

$$6aCb+2Cb^{2}=136a^{2}-4b^{2}$$

Combine all terms containing C.

$$\left(6ab+2b^{2}\right)C=136a^{2}-4b^{2}$$

Divide both sides by 6ab+2b^{2}.

$$\frac{\left(6ab+2b^{2}\right)C}{6ab+2b^{2}}=\frac{136a^{2}-4b^{2}}{6ab+2b^{2}}$$

Dividing by 6ab+2b^{2} undoes the multiplication by 6ab+2b^{2}.

$$C=\frac{136a^{2}-4b^{2}}{6ab+2b^{2}}$$

Divide 136a^{2}-4b^{2} by 6ab+2b^{2}.

$$C=\frac{2\left(34a^{2}-b^{2}\right)}{b\left(3a+b\right)}$$

Solve for a (complex solution)

$$a=\frac{\sqrt{b^{2}\left(9C^{2}+272C+544\right)}+3Cb}{136}$$

$$a=\frac{-\sqrt{b^{2}\left(9C^{2}+272C+544\right)}+3Cb}{136}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{b\left(\sqrt{9C^{2}+272C+544}+3C\right)}{136}\text{; }a=\frac{b\left(-\sqrt{9C^{2}+272C+544}+3C\right)}{136}\text{, }&C\geq \frac{20\sqrt{34}-136}{9}\text{ or }C\leq \frac{-20\sqrt{34}-136}{9}\\a=0\text{, }&b=0\end{matrix}\right.$$