Solve a*(b-c*3)=y-a

$$a \times ( b - c \times 3 ) = y - a$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{y}{b-3c+1}\text{, }&b\neq 3c-1\\a\in \mathrm{C}\text{, }&y=0\text{ and }b=3c-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Add a to both sides.

$$a\left(b-c\times 3\right)+a=y$$

Multiply -1 and 3 to get -3.

$$a\left(b-3c\right)+a=y$$

Use the distributive property to multiply a by b-3c.

$$ab-3ac+a=y$$

Combine all terms containing a.

$$\left(b-3c+1\right)a=y$$

Divide both sides by b-3c+1.

$$\frac{\left(b-3c+1\right)a}{b-3c+1}=\frac{y}{b-3c+1}$$

Dividing by b-3c+1 undoes the multiplication by b-3c+1.

$$a=\frac{y}{b-3c+1}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=3c+\frac{y}{a}-1\text{, }&a\neq 0\\b\in \mathrm{C}\text{, }&a=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply -1 and 3 to get -3.

$$a\left(b-3c\right)=y-a$$

Use the distributive property to multiply a by b-3c.

$$ab-3ac=y-a$$

Add 3ac to both sides.

$$ab=y-a+3ac$$

The equation is in standard form.

$$ab=y+3ac-a$$

Divide both sides by a.

$$\frac{ab}{a}=\frac{y+3ac-a}{a}$$

Dividing by a undoes the multiplication by a.

$$b=\frac{y+3ac-a}{a}$$

Divide y+3ac-a by a.

$$b=3c+\frac{y}{a}-1$$

Solve for a

$$\left\{\begin{matrix}a=\frac{y}{b-3c+1}\text{, }&b\neq 3c-1\\a\in \mathrm{R}\text{, }&y=0\text{ and }b=3c-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Add a to both sides.

$$a\left(b-c\times 3\right)+a=y$$

Multiply -1 and 3 to get -3.

$$a\left(b-3c\right)+a=y$$

Use the distributive property to multiply a by b-3c.

$$ab-3ac+a=y$$

Combine all terms containing a.

$$\left(b-3c+1\right)a=y$$

Divide both sides by b-3c+1.

$$\frac{\left(b-3c+1\right)a}{b-3c+1}=\frac{y}{b-3c+1}$$

Dividing by b-3c+1 undoes the multiplication by b-3c+1.

$$a=\frac{y}{b-3c+1}$$

Solve for b

$$\left\{\begin{matrix}b=3c+\frac{y}{a}-1\text{, }&a\neq 0\\b\in \mathrm{R}\text{, }&a=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply -1 and 3 to get -3.

$$a\left(b-3c\right)=y-a$$

Use the distributive property to multiply a by b-3c.

$$ab-3ac=y-a$$

Add 3ac to both sides.

$$ab=y-a+3ac$$

The equation is in standard form.

$$ab=y+3ac-a$$

Divide both sides by a.

$$\frac{ab}{a}=\frac{y+3ac-a}{a}$$

Dividing by a undoes the multiplication by a.

$$b=\frac{y+3ac-a}{a}$$

Divide y+3ac-a by a.

$$b=3c+\frac{y}{a}-1$$