d x + b = 7 ( x - d )
Solve for d (complex solution)
\left\{\begin{matrix}d=-\frac{b-7x}{x+7}\text{, }&x\neq -7\\d\in \mathrm{C}\text{, }&x=-7\text{ and }b=-49\end{matrix}\right.
Solve for b
b=-\left(dx-7x+7d\right)
Solve for d
\left\{\begin{matrix}d=-\frac{b-7x}{x+7}\text{, }&x\neq -7\\d\in \mathrm{R}\text{, }&x=-7\text{ and }b=-49\end{matrix}\right.
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dx+b=7x-7d
Use the distributive property to multiply 7 by x-d.
dx+b+7d=7x
Add 7d to both sides.
dx+7d=7x-b
Subtract b from both sides.
\left(x+7\right)d=7x-b
Combine all terms containing d.
\frac{\left(x+7\right)d}{x+7}=\frac{7x-b}{x+7}
Divide both sides by x+7.
d=\frac{7x-b}{x+7}
Dividing by x+7 undoes the multiplication by x+7.
dx+b=7x-7d
Use the distributive property to multiply 7 by x-d.
b=7x-7d-dx
Subtract dx from both sides.
dx+b=7x-7d
Use the distributive property to multiply 7 by x-d.
dx+b+7d=7x
Add 7d to both sides.
dx+7d=7x-b
Subtract b from both sides.
\left(x+7\right)d=7x-b
Combine all terms containing d.
\frac{\left(x+7\right)d}{x+7}=\frac{7x-b}{x+7}
Divide both sides by x+7.
d=\frac{7x-b}{x+7}
Dividing by x+7 undoes the multiplication by x+7.
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