Solve b+3a-6=(ab-2b)+(3a-6

$$b + 3 a - 6 = ( a b - 2 b ) + ( 3 a - 6$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=3\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ab from both sides.

$$b+3a-6-ab=-2b+3a-6$$

Subtract 3a from both sides.

$$b+3a-6-ab-3a=-2b-6$$

Combine 3a and -3a to get 0.

$$b-6-ab=-2b-6$$

Subtract b from both sides.

$$-6-ab=-2b-6-b$$

Combine -2b and -b to get -3b.

$$-6-ab=-3b-6$$

Add 6 to both sides.

$$-ab=-3b-6+6$$

Add -6 and 6 to get 0.

$$-ab=-3b$$

The equation is in standard form.

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

Divide both sides by -b.

$$\frac{\left(-b\right)a}{-b}=-\frac{3b}{-b}$$

Dividing by -b undoes the multiplication by -b.

$$a=-\frac{3b}{-b}$$

Divide -3b by -b.

$$a=3$$

Solve for b (complex solution)

$$\left\{\begin{matrix}\\b=0\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&a=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ab from both sides.

$$b+3a-6-ab=-2b+3a-6$$

Add 2b to both sides.

$$b+3a-6-ab+2b=3a-6$$

Combine b and 2b to get 3b.

$$3b+3a-6-ab=3a-6$$

Subtract 3a from both sides.

$$3b-6-ab=3a-6-3a$$

Combine 3a and -3a to get 0.

$$3b-6-ab=-6$$

Add 6 to both sides.

$$3b-ab=-6+6$$

Add -6 and 6 to get 0.

$$3b-ab=0$$

Combine all terms containing b.

$$\left(3-a\right)b=0$$

Divide 0 by 3-a.

$$b=0$$

Solve for a

$$\left\{\begin{matrix}\\a=3\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ab from both sides.

$$b+3a-6-ab=-2b+3a-6$$

Subtract 3a from both sides.

$$b+3a-6-ab-3a=-2b-6$$

Combine 3a and -3a to get 0.

$$b-6-ab=-2b-6$$

Subtract b from both sides.

$$-6-ab=-2b-6-b$$

Combine -2b and -b to get -3b.

$$-6-ab=-3b-6$$

Add 6 to both sides.

$$-ab=-3b-6+6$$

Add -6 and 6 to get 0.

$$-ab=-3b$$

The equation is in standard form.

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

Divide both sides by -b.

$$\frac{\left(-b\right)a}{-b}=-\frac{3b}{-b}$$

Dividing by -b undoes the multiplication by -b.

$$a=-\frac{3b}{-b}$$

Divide -3b by -b.

$$a=3$$

Solve for b

$$\left\{\begin{matrix}\\b=0\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&a=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ab from both sides.

$$b+3a-6-ab=-2b+3a-6$$

Add 2b to both sides.

$$b+3a-6-ab+2b=3a-6$$

Combine b and 2b to get 3b.

$$3b+3a-6-ab=3a-6$$

Subtract 3a from both sides.

$$3b-6-ab=3a-6-3a$$

Combine 3a and -3a to get 0.

$$3b-6-ab=-6$$

Add 6 to both sides.

$$3b-ab=-6+6$$

Add -6 and 6 to get 0.

$$3b-ab=0$$

Combine all terms containing b.

$$\left(3-a\right)b=0$$

Divide 0 by 3-a.

$$b=0$$