Solve for M₁ F=(GM_1M_2)/(r^2)

$F = \frac{G M_{1} M_{2}}{r^{2}}$

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

$\frac{G M_{1} M_{2}}{r^{2}} = F$

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

$\frac{G M_{1} M_{2}}{r^{2}} r^{2} = F r^{2}$

Simplify the left side.

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

Cancel the common factor.

$\frac{G M_{1} M_{2}}{r^{2}} r^{2} = F r^{2}$

Rewrite the expression.

$G M_{1} M_{2} = F r^{2}$

Divide each term in $G M_{1} M_{2} = F r^{2}$ by $G M_{2}$ and simplify.

Divide each term in $G M_{1} M_{2} = F r^{2}$ by $G M_{2}$ .

$\frac{G M_{1} M_{2}}{G M_{2}} = \frac{F r^{2}}{G M_{2}}$

Simplify the left side.

Cancel the common factor of $G$ .

Cancel the common factor.

$\frac{G M_{1} M_{2}}{G M_{2}} = \frac{F r^{2}}{G M_{2}}$

Rewrite the expression.

$\frac{M_{1} M_{2}}{M_{2}} = \frac{F r^{2}}{G M_{2}}$

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

Cancel the common factor.

$\frac{M_{1} M_{2}}{M_{2}} = \frac{F r^{2}}{G M_{2}}$

Divide $M_{1}$ by $1$ .

$M_{1} = \frac{F r^{2}}{G M_{2}}$