# How to solve for $t$ in the equation $m=-70/(t-25)$?

In the equation $$m= -\frac{70}{t-25}$$ How would I solve the equation for $t$ so that I get t equal to something $m$? I've tried multiplying both sides by $t-25$, but that just leaves me with $t=-45$. I need to have $m$ in the on the right hand side so that solution won't work.

Multiplying both sides by $t-25$ as you said gives us $$m(t-25) = -70$$ Now divide both sides by $m$ to get $$t-25 = -\frac{70}{m}$$ Simply adding $25$ to both sides gets us what we want: $$\bbox[10px, border: blue solid 1px]{t = 25 - \frac{70}{m}}$$
$$m=-\frac{70}{t-25} \Rightarrow (t-25) \cdot m= -\frac{70}{t-25} \cdot (t-25) \\ \Rightarrow (t-25) \cdot m=-70 \Rightarrow t-25=\frac{-70}{m} \Rightarrow t=25-\frac{70}{m}, m \neq 0$$