Solve 4ab-8a+6b=12

$$4 a b - 8 a + 6 b = 12$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=-\frac{3}{2}=-1.5\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&b=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 6b from both sides.

$$4ab-8a=12-6b$$

Combine all terms containing a.

$$\left(4b-8\right)a=12-6b$$

Divide both sides by 4b-8.

$$\frac{\left(4b-8\right)a}{4b-8}=\frac{12-6b}{4b-8}$$

Dividing by 4b-8 undoes the multiplication by 4b-8.

$$a=\frac{12-6b}{4b-8}$$

Divide 12-6b by 4b-8.

$$a=-\frac{3}{2}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}\\b=2\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&a=-\frac{3}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 8a to both sides.

$$4ab+6b=12+8a$$

Combine all terms containing b.

$$\left(4a+6\right)b=12+8a$$

The equation is in standard form.

$$\left(4a+6\right)b=8a+12$$

Divide both sides by 4a+6.

$$\frac{\left(4a+6\right)b}{4a+6}=\frac{8a+12}{4a+6}$$

Dividing by 4a+6 undoes the multiplication by 4a+6.

$$b=\frac{8a+12}{4a+6}$$

Divide 12+8a by 4a+6.

$$b=2$$

Solve for a

$$\left\{\begin{matrix}\\a=-\frac{3}{2}=-1.5\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&b=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 6b from both sides.

$$4ab-8a=12-6b$$

Combine all terms containing a.

$$\left(4b-8\right)a=12-6b$$

Divide both sides by 4b-8.

$$\frac{\left(4b-8\right)a}{4b-8}=\frac{12-6b}{4b-8}$$

Dividing by 4b-8 undoes the multiplication by 4b-8.

$$a=\frac{12-6b}{4b-8}$$

Divide 12-6b by 4b-8.

$$a=-\frac{3}{2}$$

Solve for b

$$\left\{\begin{matrix}\\b=2\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&a=-\frac{3}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 8a to both sides.

$$4ab+6b=12+8a$$

Combine all terms containing b.

$$\left(4a+6\right)b=12+8a$$

The equation is in standard form.

$$\left(4a+6\right)b=8a+12$$

Divide both sides by 4a+6.

$$\frac{\left(4a+6\right)b}{4a+6}=\frac{8a+12}{4a+6}$$

Dividing by 4a+6 undoes the multiplication by 4a+6.

$$b=\frac{8a+12}{4a+6}$$

Divide 12+8a by 4a+6.

$$b=2$$