Solve 4ax-b=-16a-2x

$$4 a x - b = - 16 a - 2 x$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{2x-b}{4\left(x+4\right)}\text{, }&x\neq -4\\a\in \mathrm{C}\text{, }&x=-4\text{ and }b=-8\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 16a to both sides.

$$4ax-b+16a=-2x$$

Add b to both sides.

$$4ax+16a=-2x+b$$

Combine all terms containing a.

$$\left(4x+16\right)a=-2x+b$$

The equation is in standard form.

$$\left(4x+16\right)a=b-2x$$

Divide both sides by 4x+16.

$$\frac{\left(4x+16\right)a}{4x+16}=\frac{b-2x}{4x+16}$$

Dividing by 4x+16 undoes the multiplication by 4x+16.

$$a=\frac{b-2x}{4x+16}$$

Divide -2x+b by 4x+16.

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

Solve for a

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

Steps for Solving Linear Equation

Add 16a to both sides.

$$4ax-b+16a=-2x$$

Add b to both sides.

$$4ax+16a=-2x+b$$

Combine all terms containing a.

$$\left(4x+16\right)a=-2x+b$$

The equation is in standard form.

$$\left(4x+16\right)a=b-2x$$

Divide both sides by 4x+16.

$$\frac{\left(4x+16\right)a}{4x+16}=\frac{b-2x}{4x+16}$$

Dividing by 4x+16 undoes the multiplication by 4x+16.

$$a=\frac{b-2x}{4x+16}$$

Divide -2x+b by 4x+16.

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

Solve for b

$$b=2\left(2ax+x+8a\right)$$

Steps for Solving Linear Equation

Subtract 4ax from both sides.

$$-b=-16a-2x-4ax$$

The equation is in standard form.

$$-b=-4ax-2x-16a$$

Divide both sides by -1.

$$\frac{-b}{-1}=\frac{-4ax-2x-16a}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$b=\frac{-4ax-2x-16a}{-1}$$

Divide -16a-2x-4ax by -1.

$$b=4ax+2x+16a$$