Solve for S N=S*(P-V)-F

$N = S \cdot (P - V) - F$

Rewrite the equation as $S \cdot (P - V) - F = N$ .

$S \cdot (P - V) - F = N$

Simplify each term.

Apply the distributive property.

$S P + S (- V) - F = N$

Rewrite using the commutative property of multiplication.

$S P - S V - F = N$

Add $F$ to both sides of the equation.

$S P - S V = N + F$

Factor $S$ out of $S P - S V$ .

Factor $S$ out of $S P$ .

$S (P) - S V = N + F$

Factor $S$ out of $- S V$ .

$S (P) + S (- 1 V) = N + F$

Factor $S$ out of $S (P) + S (- 1 V)$ .

$S (P - 1 V) = N + F$

Rewrite $- 1 V$ as $- V$ .

$S (P - V) = N + F$

Divide each term in $S (P - V) = N + F$ by $P - V$ and simplify.

Divide each term in $S (P - V) = N + F$ by $P - V$ .

$\frac{S (P - V)}{P - V} = \frac{N}{P - V} + \frac{F}{P - V}$

Simplify the left side.

Cancel the common factor of $P - V$ .

Cancel the common factor.

$\frac{S (P - V)}{P - V} = \frac{N}{P - V} + \frac{F}{P - V}$

Divide $S$ by $1$ .

$S = \frac{N}{P - V} + \frac{F}{P - V}$

Simplify the right side.

Combine the numerators over the common denominator.

$S = \frac{N + F}{P - V}$