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