Solve for m
\left\{\begin{matrix}m=\frac{t}{x+z}\text{, }&x\neq -z\\m\in \mathrm{R}\text{, }&t=0\text{ and }x=-z\end{matrix}\right.
Solve for t
t=m\left(x+z\right)
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t=xm+zm
Use the distributive property to multiply x+z by m.
xm+zm=t
Swap sides so that all variable terms are on the left hand side.
\left(x+z\right)m=t
Combine all terms containing m.
\frac{\left(x+z\right)m}{x+z}=\frac{t}{x+z}
Divide both sides by x+z.
m=\frac{t}{x+z}
Dividing by x+z undoes the multiplication by x+z.
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