Solve 8a+4b+2c+ab=23

$$8 a + 4 b + 2 c + a b = 23$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{4b+2c-23}{b+8}\text{, }&b\neq -8\\a\in \mathrm{R}\text{, }&b=-8\text{ and }c=\frac{55}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4b from both sides.

$$8a+2c+ab=23-4b$$

Subtract 2c from both sides.

$$8a+ab=23-4b-2c$$

Combine all terms containing a.

$$\left(8+b\right)a=23-4b-2c$$

The equation is in standard form.

$$\left(b+8\right)a=23-2c-4b$$

Divide both sides by 8+b.

$$\frac{\left(b+8\right)a}{b+8}=\frac{23-2c-4b}{b+8}$$

Dividing by 8+b undoes the multiplication by 8+b.

$$a=\frac{23-2c-4b}{b+8}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{8a+2c-23}{a+4}\text{, }&a\neq -4\\b\in \mathrm{R}\text{, }&a=-4\text{ and }c=\frac{55}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 8a from both sides.

$$4b+2c+ab=23-8a$$

Subtract 2c from both sides.

$$4b+ab=23-8a-2c$$

Combine all terms containing b.

$$\left(4+a\right)b=23-8a-2c$$

The equation is in standard form.

$$\left(a+4\right)b=23-2c-8a$$

Divide both sides by 4+a.

$$\frac{\left(a+4\right)b}{a+4}=\frac{23-2c-8a}{a+4}$$

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

$$b=\frac{23-2c-8a}{a+4}$$