Solve for b (complex solution)
\left\{\begin{matrix}b=-x+\frac{p}{m}\text{, }&m\neq 0\\b\in \mathrm{C}\text{, }&p=0\text{ and }m=0\end{matrix}\right.
Solve for m (complex solution)
\left\{\begin{matrix}m=\frac{p}{x+b}\text{, }&x\neq -b\\m\in \mathrm{C}\text{, }&p=0\text{ and }x=-b\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=-x+\frac{p}{m}\text{, }&m\neq 0\\b\in \mathrm{R}\text{, }&p=0\text{ and }m=0\end{matrix}\right.
Solve for m
\left\{\begin{matrix}m=\frac{p}{x+b}\text{, }&x\neq -b\\m\in \mathrm{R}\text{, }&p=0\text{ and }x=-b\end{matrix}\right.
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mb=p-mx
Subtract mx from both sides.
\frac{mb}{m}=\frac{p-mx}{m}
Divide both sides by m.
b=\frac{p-mx}{m}
Dividing by m undoes the multiplication by m.
b=-x+\frac{p}{m}
Divide p-mx by m.
\left(x+b\right)m=p
Combine all terms containing m.
\frac{\left(x+b\right)m}{x+b}=\frac{p}{x+b}
Divide both sides by x+b.
m=\frac{p}{x+b}
Dividing by x+b undoes the multiplication by x+b.
mb=p-mx
Subtract mx from both sides.
\frac{mb}{m}=\frac{p-mx}{m}
Divide both sides by m.
b=\frac{p-mx}{m}
Dividing by m undoes the multiplication by m.
b=-x+\frac{p}{m}
Divide p-mx by m.
\left(x+b\right)m=p
Combine all terms containing m.
\frac{\left(x+b\right)m}{x+b}=\frac{p}{x+b}
Divide both sides by x+b.
m=\frac{p}{x+b}
Dividing by x+b undoes the multiplication by x+b.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}