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