Solve for a (complex solution)
\left\{\begin{matrix}a=-\frac{-2cx+b-2d}{x}\text{, }&x\neq 0\text{ and }d\neq -cx\\a\in \mathrm{C}\text{, }&d=\frac{b}{2}\text{ and }x=0\text{ and }b\neq 0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=-\frac{-2cx+b-2d}{x}\text{, }&x\neq 0\text{ and }d\neq -cx\\a\in \mathrm{R}\text{, }&d=\frac{b}{2}\text{ and }x=0\text{ and }b\neq 0\end{matrix}\right.
Solve for b
b=2d+2cx-ax
d\neq -cx
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ax+b=2\left(cx+d\right)
Multiply both sides of the equation by cx+d.
ax+b=2cx+2d
Use the distributive property to multiply 2 by cx+d.
ax=2cx+2d-b
Subtract b from both sides.
xa=2cx+2d-b
The equation is in standard form.
\frac{xa}{x}=\frac{2cx+2d-b}{x}
Divide both sides by x.
a=\frac{2cx+2d-b}{x}
Dividing by x undoes the multiplication by x.
ax+b=2\left(cx+d\right)
Multiply both sides of the equation by cx+d.
ax+b=2cx+2d
Use the distributive property to multiply 2 by cx+d.
ax=2cx+2d-b
Subtract b from both sides.
xa=2cx+2d-b
The equation is in standard form.
\frac{xa}{x}=\frac{2cx+2d-b}{x}
Divide both sides by x.
a=\frac{2cx+2d-b}{x}
Dividing by x undoes the multiplication by x.
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