Solve -48b^2+105c^2+104Bc=0

$$- 48 b ^ { 2 } + 105 c ^ { 2 } + 104 B c = 0$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B=\frac{6b^{2}}{13c}-\frac{105c}{104}\text{, }&c\neq 0\\B\in \mathrm{C}\text{, }&b=0\text{ and }c=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 48b^{2} to both sides. Anything plus zero gives itself.

$$105c^{2}+104Bc=48b^{2}$$

Subtract 105c^{2} from both sides.

$$104Bc=48b^{2}-105c^{2}$$

The equation is in standard form.

$$104cB=48b^{2}-105c^{2}$$

Divide both sides by 104c.

$$\frac{104cB}{104c}=\frac{48b^{2}-105c^{2}}{104c}$$

Dividing by 104c undoes the multiplication by 104c.

$$B=\frac{48b^{2}-105c^{2}}{104c}$$

Divide 48b^{2}-105c^{2} by 104c.

$$B=\frac{6b^{2}}{13c}-\frac{105c}{104}$$

Solve for B

$$\left\{\begin{matrix}B=\frac{6b^{2}}{13c}-\frac{105c}{104}\text{, }&c\neq 0\\B\in \mathrm{R}\text{, }&b=0\text{ and }c=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 48b^{2} to both sides. Anything plus zero gives itself.

$$105c^{2}+104Bc=48b^{2}$$

Subtract 105c^{2} from both sides.

$$104Bc=48b^{2}-105c^{2}$$

The equation is in standard form.

$$104cB=48b^{2}-105c^{2}$$

Divide both sides by 104c.

$$\frac{104cB}{104c}=\frac{48b^{2}-105c^{2}}{104c}$$

Dividing by 104c undoes the multiplication by 104c.

$$B=\frac{48b^{2}-105c^{2}}{104c}$$

Divide 48b^{2}-105c^{2} by 104c.

$$B=\frac{6b^{2}}{13c}-\frac{105c}{104}$$

Solve for b (complex solution)

$$b=-\frac{\sqrt{3c\left(104B+105c\right)}}{12}$$

$$b=\frac{\sqrt{3c\left(104B+105c\right)}}{12}$$

Solve for b

$$b=\frac{\sqrt{3c\left(104B+105c\right)}}{12}$$

$$b=-\frac{\sqrt{3c\left(104B+105c\right)}}{12}\text{, }\left(c\geq 0\text{ or }c\leq -\frac{104B}{105}\right)\text{ and }\left(c\leq 0\text{ or }c\geq -\frac{104B}{105}\right)$$