Solve for m₁ F=G((m_1m_2)/(d^2))

$F = G (\frac{m_{1} m_{2}}{d^{2}})$

Step 1

Rewrite the equation as $G \frac{m_{1} m_{2}}{d^{2}} = F$ .

$G \frac{m_{1} m_{2}}{d^{2}} = F$

Step 2

Simplify.

Combine $G$ and $\frac{m_{1} m_{2}}{d^{2}}$ .

$\frac{G (m_{1} m_{2})}{d^{2}} = F$

Remove parentheses.

$\frac{G m_{1} m_{2}}{d^{2}} = F$

Step 3

Divide each term in $\frac{G m_{1} m_{2}}{d^{2}} = F$ by $G$ and simplify.

Divide each term in $\frac{G m_{1} m_{2}}{d^{2}} = F$ by $G$ .

$\frac{\frac{G m_{1} m_{2}}{d^{2}}}{G} = \frac{F}{G}$

Simplify the left side.

Multiply the numerator by the reciprocal of the denominator.

$\frac{G m_{1} m_{2}}{d^{2}} \cdot \frac{1}{G} = \frac{F}{G}$

Combine.

$\frac{G m_{1} m_{2} \cdot 1}{d^{2} G} = \frac{F}{G}$

Cancel the common factor of $G$ .

Cancel the common factor.

$\frac{G m_{1} m_{2} \cdot 1}{d^{2} G} = \frac{F}{G}$

Rewrite the expression.

$\frac{m_{1} m_{2} \cdot 1}{d^{2}} = \frac{F}{G}$

Multiply $m_{1}$ by $1$ .

$\frac{m_{1} m_{2}}{d^{2}} = \frac{F}{G}$

Step 4

Multiply both sides by $d^{2}$ .

$\frac{m_{1} m_{2}}{d^{2}} d^{2} = \frac{F}{G} d^{2}$

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $d^{2}$ .

Cancel the common factor.

$\frac{m_{1} m_{2}}{d^{2}} d^{2} = \frac{F}{G} d^{2}$

Rewrite the expression.

$m_{1} m_{2} = \frac{F}{G} d^{2}$

Simplify the right side.

Combine $\frac{F}{G}$ and $d^{2}$ .

$m_{1} m_{2} = \frac{F d^{2}}{G}$

Step 6

Divide each term in $m_{1} m_{2} = \frac{F d^{2}}{G}$ by $m_{2}$ and simplify.

Divide each term in $m_{1} m_{2} = \frac{F d^{2}}{G}$ by $m_{2}$ .

$\frac{m_{1} m_{2}}{m_{2}} = \frac{\frac{F d^{2}}{G}}{m_{2}}$

Simplify the left side.

Cancel the common factor of $m_{2}$ .

Cancel the common factor.

$\frac{m_{1} m_{2}}{m_{2}} = \frac{\frac{F d^{2}}{G}}{m_{2}}$

Divide $m_{1}$ by $1$ .

$m_{1} = \frac{\frac{F d^{2}}{G}}{m_{2}}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$m_{1} = \frac{F d^{2}}{G} \cdot \frac{1}{m_{2}}$

Combine.

$m_{1} = \frac{F d^{2} \cdot 1}{G m_{2}}$

Multiply $F$ by $1$ .

$m_{1} = \frac{F d^{2}}{G m_{2}}$

Solve for m₁ F=G((m_1m_2)/(d^2))

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