Solve ma=mg-bv

$$m a = m g - b v$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

The equation is in standard form.

$$ma=gm-bv$$

Divide both sides by m.

$$\frac{ma}{m}=\frac{gm-bv}{m}$$

Dividing by m undoes the multiplication by m.

$$a=\frac{gm-bv}{m}$$

Divide mg-bv by m.

$$a=-\frac{bv}{m}+g$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

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

$$mg-bv=ma$$

Subtract mg from both sides.

$$-bv=ma-mg$$

The equation is in standard form.

$$\left(-v\right)b=am-gm$$

Divide both sides by -v.

$$\frac{\left(-v\right)b}{-v}=\frac{m\left(a-g\right)}{-v}$$

Dividing by -v undoes the multiplication by -v.

$$b=\frac{m\left(a-g\right)}{-v}$$

Divide m\left(a-g\right) by -v.

$$b=-\frac{m\left(a-g\right)}{v}$$

Solve for a

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

Steps for Solving Linear Equation

The equation is in standard form.

$$ma=gm-bv$$

Divide both sides by m.

$$\frac{ma}{m}=\frac{gm-bv}{m}$$

Dividing by m undoes the multiplication by m.

$$a=\frac{gm-bv}{m}$$

Divide mg-bv by m.

$$a=-\frac{bv}{m}+g$$

Solve for b

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

Steps for Solving Linear Equation

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

$$mg-bv=ma$$

Subtract mg from both sides.

$$-bv=ma-mg$$

The equation is in standard form.

$$\left(-v\right)b=am-gm$$

Divide both sides by -v.

$$\frac{\left(-v\right)b}{-v}=\frac{m\left(a-g\right)}{-v}$$

Dividing by -v undoes the multiplication by -v.

$$b=\frac{m\left(a-g\right)}{-v}$$

Divide m\left(a-g\right) by -v.

$$b=-\frac{m\left(a-g\right)}{v}$$