Solve for r F=G(mM)/(r^2)

$F = G \frac{m M}{r^{2}}$

Rewrite the equation as $G (\frac{m M}{r^{2}}) = F$ .

$G (\frac{m M}{r^{2}}) = F$

Combine $G$ and $\frac{m M}{r^{2}}$ .

$\frac{G m M}{r^{2}} = F$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$r^{2}, 1$

The LCM of one and any expression is the expression.

$r^{2}$

Multiply each term in $\frac{G m M}{r^{2}} = F$ by $r^{2}$ to eliminate the fractions.

Multiply each term in $\frac{G m M}{r^{2}} = F$ by $r^{2}$ .

$\frac{G m M}{r^{2}} r^{2} = F r^{2}$

Simplify the left side.

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

Cancel the common factor.

$\frac{G m M}{r^{2}} r^{2} = F r^{2}$

Rewrite the expression.

$G m M = F r^{2}$

Solve the equation.

Rewrite the equation as $F r^{2} = G m M$ .

$F r^{2} = G m M$

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

Divide each term in $F r^{2} = G m M$ by $F$ .

$\frac{F r^{2}}{F} = \frac{G m M}{F}$

Simplify the left side.

Cancel the common factor of $F$ .

Cancel the common factor.

$\frac{F r^{2}}{F} = \frac{G m M}{F}$

Divide $r^{2}$ by $1$ .

$r^{2} = \frac{G m M}{F}$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$r = \pm \sqrt{\frac{G m M}{F}}$

Simplify $\pm \sqrt{\frac{G m M}{F}}$ .

Rewrite $\sqrt{\frac{G m M}{F}}$ as $\frac{\sqrt{G m M}}{\sqrt{F}}$ .

$r = \pm \frac{\sqrt{G m M}}{\sqrt{F}}$

Multiply $\frac{\sqrt{G m M}}{\sqrt{F}}$ by $\frac{\sqrt{F}}{\sqrt{F}}$ .

$r = \pm \frac{\sqrt{G m M}}{\sqrt{F}} \cdot \frac{\sqrt{F}}{\sqrt{F}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{G m M}}{\sqrt{F}}$ by $\frac{\sqrt{F}}{\sqrt{F}}$ .

$r = \pm \frac{\sqrt{G m M} \sqrt{F}}{\sqrt{F} \sqrt{F}}$

Raise $\sqrt{F}$ to the power of $1$ .

$r = \pm \frac{\sqrt{G m M} \sqrt{F}}{{\sqrt{F}}^{1} \sqrt{F}}$

Raise $\sqrt{F}$ to the power of $1$ .

$r = \pm \frac{\sqrt{G m M} \sqrt{F}}{{\sqrt{F}}^{1} {\sqrt{F}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$r = \pm \frac{\sqrt{G m M} \sqrt{F}}{{\sqrt{F}}^{1 + 1}}$

Add $1$ and $1$ .

$r = \pm \frac{\sqrt{G m M} \sqrt{F}}{{\sqrt{F}}^{2}}$

Rewrite ${\sqrt{F}}^{2}$ as $F$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{F}$ as $F^{\frac{1}{2}}$ .

$r = \pm \frac{\sqrt{G m M} \sqrt{F}}{{(F^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$r = \pm \frac{\sqrt{G m M} \sqrt{F}}{F^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$r = \pm \frac{\sqrt{G m M} \sqrt{F}}{F^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$r = \pm \frac{\sqrt{G m M} \sqrt{F}}{F^{\frac{2}{2}}}$

Rewrite the expression.

$r = \pm \frac{\sqrt{G m M} \sqrt{F}}{F^{1}}$

Simplify.

$r = \pm \frac{\sqrt{G m M} \sqrt{F}}{F}$

Combine using the product rule for radicals.

$r = \pm \frac{\sqrt{G m M F}}{F}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$r = \frac{\sqrt{G m M F}}{F}$

Next, use the negative value of the $\pm$ to find the second solution.

$r = - \frac{\sqrt{G m M F}}{F}$

The complete solution is the result of both the positive and negative portions of the solution.

$r = \frac{\sqrt{G m M F}}{F}$

$r = - \frac{\sqrt{G m M F}}{F}$

$r = \frac{\sqrt{G m M F}}{F}$

$r = - \frac{\sqrt{G m M F}}{F}$

$r = \frac{\sqrt{G m M F}}{F}$

$r = - \frac{\sqrt{G m M F}}{F}$

Solve for r F=G(mM)/(r^2)

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