Solve for m ma=fapp-mg

$m a = f a p \cdot p - mg$

Multiply $p$ by $p$ by adding the exponents.

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Move $p$ .

$m a = f a (p \cdot p) - m g$

Multiply $p$ by $p$ .

$m a = f a p^{2} - m g$

Add $m g$ to both sides of the equation.

$m a + m g = f a p^{2}$

Factor $m$ out of $m a + m g$ .

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Factor $m$ out of $m a$ .

$m (a) + m g = f a p^{2}$

Factor $m$ out of $m g$ .

$m (a) + m (g) = f a p^{2}$

Factor $m$ out of $m (a) + m (g)$ .

$m (a + g) = f a p^{2}$

Divide each term by $a + g$ and simplify.

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Divide each term in $m (a + g) = f a p^{2}$ by $a + g$ .

$\frac{m (a + g)}{a + g} = \frac{f a p^{2}}{a + g}$

Cancel the common factor of $a + g$ .

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Cancel the common factor.

$\frac{m (a + g)}{a + g} = \frac{f a p^{2}}{a + g}$

Divide $m$ by $1$ .

$m = \frac{f a p^{2}}{a + g}$

Solve for m ma=fapp-mg