Solve x=4a+2b+ab-7a+2

$$x = 4 a + 2 b + a b - 7 a + 2$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{2+2b-x}{b-3}\text{, }&b\neq 3\\a\in \mathrm{C}\text{, }&x=8\text{ and }b=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 4a and -7a to get -3a.

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

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

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

Subtract 2b from both sides.

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

Subtract 2 from both sides.

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

Combine all terms containing a.

$$\left(-3+b\right)a=x-2b-2$$

The equation is in standard form.

$$\left(b-3\right)a=x-2b-2$$

Divide both sides by -3+b.

$$\frac{\left(b-3\right)a}{b-3}=\frac{x-2b-2}{b-3}$$

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

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

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{2-3a-x}{a+2}\text{, }&a\neq -2\\b\in \mathrm{C}\text{, }&x=8\text{ and }a=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 4a and -7a to get -3a.

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

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

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

Add 3a to both sides.

$$2b+ab+2=x+3a$$

Subtract 2 from both sides.

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

Combine all terms containing b.

$$\left(2+a\right)b=x+3a-2$$

The equation is in standard form.

$$\left(a+2\right)b=x+3a-2$$

Divide both sides by 2+a.

$$\frac{\left(a+2\right)b}{a+2}=\frac{x+3a-2}{a+2}$$

Dividing by 2+a undoes the multiplication by 2+a.

$$b=\frac{x+3a-2}{a+2}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{2+2b-x}{b-3}\text{, }&b\neq 3\\a\in \mathrm{R}\text{, }&x=8\text{ and }b=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 4a and -7a to get -3a.

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

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

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

Subtract 2b from both sides.

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

Subtract 2 from both sides.

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

Combine all terms containing a.

$$\left(-3+b\right)a=x-2b-2$$

The equation is in standard form.

$$\left(b-3\right)a=x-2b-2$$

Divide both sides by -3+b.

$$\frac{\left(b-3\right)a}{b-3}=\frac{x-2b-2}{b-3}$$

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

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

Solve for b

$$\left\{\begin{matrix}b=-\frac{2-3a-x}{a+2}\text{, }&a\neq -2\\b\in \mathrm{R}\text{, }&x=8\text{ and }a=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 4a and -7a to get -3a.

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

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

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

Add 3a to both sides.

$$2b+ab+2=x+3a$$

Subtract 2 from both sides.

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

Combine all terms containing b.

$$\left(2+a\right)b=x+3a-2$$

The equation is in standard form.

$$\left(a+2\right)b=x+3a-2$$

Divide both sides by 2+a.

$$\frac{\left(a+2\right)b}{a+2}=\frac{x+3a-2}{a+2}$$

Dividing by 2+a undoes the multiplication by 2+a.

$$b=\frac{x+3a-2}{a+2}$$