Solve for g T=gr+gvt

$T = g r + g v t$

Step 1

Rewrite the equation as $g r + g v t = T$ .

$g r + g v t = T$

Step 2

Factor $g$ out of $g r + g v t$ .

Factor $g$ out of $g r$ .

$g (r) + g v t = T$

Factor $g$ out of $g v t$ .

$g (r) + g (v t) = T$

Factor $g$ out of $g (r) + g (v t)$ .

$g (r + v t) = T$

Step 3

Divide each term in $g (r + v t) = T$ by $r + v t$ and simplify.

Divide each term in $g (r + v t) = T$ by $r + v t$ .

$\frac{g (r + v t)}{r + v t} = \frac{T}{r + v t}$

Simplify the left side.

Cancel the common factor of $r + v t$ .

Cancel the common factor.

$\frac{g (r + v t)}{r + v t} = \frac{T}{r + v t}$

Divide $g$ by $1$ .

$g = \frac{T}{r + v t}$