Solve (2a-b)*x+a+b+12=0

$$( 2 a - b ) \cdot x + a + b + 12 = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{12+b-bx}{2x+1}\text{, }&x\neq -\frac{1}{2}\\a\in \mathrm{C}\text{, }&x=-\frac{1}{2}\text{ and }b=-8\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2a-b by x.

$$2ax-bx+a+b+12=0$$

Add bx to both sides. Anything plus zero gives itself.

$$2ax+a+b+12=bx$$

Subtract b from both sides.

$$2ax+a+12=bx-b$$

Subtract 12 from both sides.

$$2ax+a=bx-b-12$$

Combine all terms containing a.

$$\left(2x+1\right)a=bx-b-12$$

Divide both sides by 2x+1.

$$\frac{\left(2x+1\right)a}{2x+1}=\frac{bx-b-12}{2x+1}$$

Dividing by 2x+1 undoes the multiplication by 2x+1.

$$a=\frac{bx-b-12}{2x+1}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{2ax+a+12}{1-x}\text{, }&x\neq 1\\b\in \mathrm{C}\text{, }&x=1\text{ and }a=-4\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2a-b by x.

$$2ax-bx+a+b+12=0$$

Subtract 2ax from both sides. Anything subtracted from zero gives its negation.

$$-bx+a+b+12=-2ax$$

Subtract a from both sides.

$$-bx+b+12=-2ax-a$$

Subtract 12 from both sides.

$$-bx+b=-2ax-a-12$$

Combine all terms containing b.

$$\left(-x+1\right)b=-2ax-a-12$$

The equation is in standard form.

$$\left(1-x\right)b=-2ax-a-12$$

Divide both sides by -x+1.

$$\frac{\left(1-x\right)b}{1-x}=\frac{-2ax-a-12}{1-x}$$

Dividing by -x+1 undoes the multiplication by -x+1.

$$b=\frac{-2ax-a-12}{1-x}$$

Divide -2ax-a-12 by -x+1.

$$b=-\frac{2ax+a+12}{1-x}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{12+b-bx}{2x+1}\text{, }&x\neq -\frac{1}{2}\\a\in \mathrm{R}\text{, }&x=-\frac{1}{2}\text{ and }b=-8\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2a-b by x.

$$2ax-bx+a+b+12=0$$

Add bx to both sides. Anything plus zero gives itself.

$$2ax+a+b+12=bx$$

Subtract b from both sides.

$$2ax+a+12=bx-b$$

Subtract 12 from both sides.

$$2ax+a=bx-b-12$$

Combine all terms containing a.

$$\left(2x+1\right)a=bx-b-12$$

Divide both sides by 2x+1.

$$\frac{\left(2x+1\right)a}{2x+1}=\frac{bx-b-12}{2x+1}$$

Dividing by 2x+1 undoes the multiplication by 2x+1.

$$a=\frac{bx-b-12}{2x+1}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{2ax+a+12}{1-x}\text{, }&x\neq 1\\b\in \mathrm{R}\text{, }&x=1\text{ and }a=-4\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2a-b by x.

$$2ax-bx+a+b+12=0$$

Subtract 2ax from both sides. Anything subtracted from zero gives its negation.

$$-bx+a+b+12=-2ax$$

Subtract a from both sides.

$$-bx+b+12=-2ax-a$$

Subtract 12 from both sides.

$$-bx+b=-2ax-a-12$$

Combine all terms containing b.

$$\left(-x+1\right)b=-2ax-a-12$$

The equation is in standard form.

$$\left(1-x\right)b=-2ax-a-12$$

Divide both sides by -x+1.

$$\frac{\left(1-x\right)b}{1-x}=\frac{-2ax-a-12}{1-x}$$

Dividing by -x+1 undoes the multiplication by -x+1.

$$b=\frac{-2ax-a-12}{1-x}$$

Divide -2ax-a-12 by -x+1.

$$b=-\frac{2ax+a+12}{1-x}$$