Solve for a
\left\{\begin{matrix}a=cp+\frac{np}{x}-b\text{, }&p\neq 0\text{ and }x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }n=0\text{ and }p\neq 0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=cp+\frac{np}{x}-a\text{, }&p\neq 0\text{ and }x\neq 0\\b\in \mathrm{R}\text{, }&x=0\text{ and }n=0\text{ and }p\neq 0\end{matrix}\right.
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ax+bx=pn+cxp
Multiply both sides of the equation by p.
ax=pn+cxp-bx
Subtract bx from both sides.
xa=cpx-bx+np
The equation is in standard form.
\frac{xa}{x}=\frac{cpx-bx+np}{x}
Divide both sides by x.
a=\frac{cpx-bx+np}{x}
Dividing by x undoes the multiplication by x.
a=cp+\frac{np}{x}-b
Divide pn+cxp-bx by x.
ax+bx=pn+cxp
Multiply both sides of the equation by p.
bx=pn+cxp-ax
Subtract ax from both sides.
xb=cpx-ax+np
The equation is in standard form.
\frac{xb}{x}=\frac{cpx-ax+np}{x}
Divide both sides by x.
b=\frac{cpx-ax+np}{x}
Dividing by x undoes the multiplication by x.
b=cp+\frac{np}{x}-a
Divide pn+cxp-ax by x.
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