Solve for n (complex solution)
\left\{\begin{matrix}n=\frac{4b-x}{4\left(x+1\right)}\text{, }&x\neq -1\\n\in \mathrm{C}\text{, }&x=-1\text{ and }b=-\frac{1}{4}\end{matrix}\right.
Solve for b
b=nx+\frac{x}{4}+n
Solve for n
\left\{\begin{matrix}n=\frac{4b-x}{4\left(x+1\right)}\text{, }&x\neq -1\\n\in \mathrm{R}\text{, }&x=-1\text{ and }b=-\frac{1}{4}\end{matrix}\right.
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-x+4b=4n\left(x+1\right)
Multiply both sides of the equation by 4.
-x+4b=4nx+4n
Use the distributive property to multiply 4n by x+1.
4nx+4n=-x+4b
Swap sides so that all variable terms are on the left hand side.
\left(4x+4\right)n=-x+4b
Combine all terms containing n.
\left(4x+4\right)n=4b-x
The equation is in standard form.
\frac{\left(4x+4\right)n}{4x+4}=\frac{4b-x}{4x+4}
Divide both sides by 4x+4.
n=\frac{4b-x}{4x+4}
Dividing by 4x+4 undoes the multiplication by 4x+4.
n=\frac{4b-x}{4\left(x+1\right)}
Divide -x+4b by 4x+4.
-x+4b=4n\left(x+1\right)
Multiply both sides of the equation by 4.
-x+4b=4nx+4n
Use the distributive property to multiply 4n by x+1.
4b=4nx+4n+x
Add x to both sides.
4b=4nx+x+4n
The equation is in standard form.
\frac{4b}{4}=\frac{4nx+x+4n}{4}
Divide both sides by 4.
b=\frac{4nx+x+4n}{4}
Dividing by 4 undoes the multiplication by 4.
b=nx+\frac{x}{4}+n
Divide 4nx+4n+x by 4.
-x+4b=4n\left(x+1\right)
Multiply both sides of the equation by 4.
-x+4b=4nx+4n
Use the distributive property to multiply 4n by x+1.
4nx+4n=-x+4b
Swap sides so that all variable terms are on the left hand side.
\left(4x+4\right)n=-x+4b
Combine all terms containing n.
\left(4x+4\right)n=4b-x
The equation is in standard form.
\frac{\left(4x+4\right)n}{4x+4}=\frac{4b-x}{4x+4}
Divide both sides by 4x+4.
n=\frac{4b-x}{4x+4}
Dividing by 4x+4 undoes the multiplication by 4x+4.
n=\frac{4b-x}{4\left(x+1\right)}
Divide -x+4b by 4x+4.
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