Solve d=a(x-c)/b

$$d = \frac { a ( x - c ) } { b }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{bd}{x-c}\text{, }&x\neq c\text{ and }b\neq 0\\a\in \mathrm{C}\text{, }&d=0\text{ and }x=c\text{ and }b\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by b.

$$db=a\left(x-c\right)$$

Use the distributive property to multiply a by x-c.

$$db=ax-ac$$

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

$$ax-ac=db$$

Combine all terms containing a.

$$\left(x-c\right)a=db$$

The equation is in standard form.

$$\left(x-c\right)a=bd$$

Divide both sides by x-c.

$$\frac{\left(x-c\right)a}{x-c}=\frac{bd}{x-c}$$

Dividing by x-c undoes the multiplication by x-c.

$$a=\frac{bd}{x-c}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{bd}{x-c}\text{, }&x\neq c\text{ and }b\neq 0\\a\in \mathrm{R}\text{, }&d=0\text{ and }x=c\text{ and }b\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by b.

$$db=a\left(x-c\right)$$

Use the distributive property to multiply a by x-c.

$$db=ax-ac$$

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

$$ax-ac=db$$

Combine all terms containing a.

$$\left(x-c\right)a=db$$

The equation is in standard form.

$$\left(x-c\right)a=bd$$

Divide both sides by x-c.

$$\frac{\left(x-c\right)a}{x-c}=\frac{bd}{x-c}$$

Dividing by x-c undoes the multiplication by x-c.

$$a=\frac{bd}{x-c}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{a\left(x-c\right)}{d}\text{, }&x\neq c\text{ and }a\neq 0\text{ and }d\neq 0\\b\neq 0\text{, }&\left(x=c\text{ or }a=0\right)\text{ and }d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$db=a\left(x-c\right)$$

Use the distributive property to multiply a by x-c.

$$db=ax-ac$$

Divide both sides by d.

$$\frac{db}{d}=\frac{a\left(x-c\right)}{d}$$

Dividing by d undoes the multiplication by d.

$$b=\frac{a\left(x-c\right)}{d}$$

Variable b cannot be equal to 0.

$$b=\frac{a\left(x-c\right)}{d}\text{, }b\neq 0$$