Solve for t p=s_1t-s_2t

$p = s_{1} t - s_{2} t$

Step 1

Rewrite the equation as $s_{1} t - s_{2} t = p$ .

$s_{1} t - s_{2} t = p$

Step 2

Factor $t$ out of $s_{1} t - s_{2} t$ .

Factor $t$ out of $s_{1} t$ .

$t s_{1} - s_{2} t = p$

Factor $t$ out of $- s_{2} t$ .

$t s_{1} + t (- s_{2}) = p$

Factor $t$ out of $t s_{1} + t (- s_{2})$ .

$t (s_{1} - s_{2}) = p$

Step 3

Divide each term in $t (s_{1} - s_{2}) = p$ by $s_{1} - s_{2}$ and simplify.

Divide each term in $t (s_{1} - s_{2}) = p$ by $s_{1} - s_{2}$ .

$\frac{t (s_{1} - s_{2})}{s_{1} - s_{2}} = \frac{p}{s_{1} - s_{2}}$

Simplify the left side.

Cancel the common factor of $s_{1} - s_{2}$ .

Cancel the common factor.

$\frac{t (s_{1} - s_{2})}{s_{1} - s_{2}} = \frac{p}{s_{1} - s_{2}}$

Divide $t$ by $1$ .

$t = \frac{p}{s_{1} - s_{2}}$