Solve alphabeta=C/a

$$\alpha \beta = \frac { C } { a }$$

Solve for C

$$C=a\alpha \beta$$

$$a\neq 0$$

Solution Steps

Multiply both sides of the equation by a.

$$\alpha \beta a=C$$

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

$$C=\alpha \beta a$$

Solve for a

$$\left\{\begin{matrix}a=\frac{C}{\alpha \beta }\text{, }&C\neq 0\text{ and }\beta \neq 0\text{ and }\alpha \neq 0\\a\neq 0\text{, }&\left(\alpha =0\text{ or }\beta =0\right)\text{ and }C=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$\alpha \beta a=C$$

Divide both sides by \alpha \beta .

$$\frac{\alpha \beta a}{\alpha \beta }=\frac{C}{\alpha \beta }$$

Dividing by \alpha \beta undoes the multiplication by \alpha \beta .

$$a=\frac{C}{\alpha \beta }$$

Variable a cannot be equal to 0.

$$a=\frac{C}{\alpha \beta }\text{, }a\neq 0$$