Solve θF-32/212-32=GM-20/220-20

$$\frac { \theta F - 32 } { 212 - 32 } = \frac { G M - 20 } { 220 - 20 }$$

Solve for F (complex solution)

$$\left\{\begin{matrix}F=\frac{9GM+140}{10\theta }\text{, }&\theta \neq 0\\F\in \mathrm{C}\text{, }&G=-\frac{140}{9M}\text{ and }M\neq 0\text{ and }\theta =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 32 from 212 to get 180.

$$\frac{\theta F-32}{180}=\frac{GM-20}{220-20}$$

Subtract 20 from 220 to get 200.

$$\frac{\theta F-32}{180}=\frac{GM-20}{200}$$

Multiply both sides of the equation by 1800, the least common multiple of 180,200.

$$10\left(\theta F-32\right)=9\left(GM-20\right)$$

Use the distributive property to multiply 10 by \theta F-32.

$$10\theta F-320=9\left(GM-20\right)$$

Use the distributive property to multiply 9 by GM-20.

$$10\theta F-320=9GM-180$$

Add 320 to both sides.

$$10\theta F=9GM-180+320$$

Add -180 and 320 to get 140.

$$10\theta F=9GM+140$$

Divide both sides by 10\theta .

$$\frac{10\theta F}{10\theta }=\frac{9GM+140}{10\theta }$$

Dividing by 10\theta undoes the multiplication by 10\theta .

$$F=\frac{9GM+140}{10\theta }$$

Solve for G (complex solution)

$$\left\{\begin{matrix}G=-\frac{10\left(14-F\theta \right)}{9M}\text{, }&M\neq 0\\G\in \mathrm{C}\text{, }&\theta =\frac{14}{F}\text{ and }F\neq 0\text{ and }M=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 32 from 212 to get 180.

$$\frac{\theta F-32}{180}=\frac{GM-20}{220-20}$$

Subtract 20 from 220 to get 200.

$$\frac{\theta F-32}{180}=\frac{GM-20}{200}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{GM-20}{200}=\frac{\theta F-32}{180}$$

Multiply both sides of the equation by 1800, the least common multiple of 200,180.

$$9\left(GM-20\right)=10\left(\theta F-32\right)$$

Use the distributive property to multiply 9 by GM-20.

$$9GM-180=10\left(\theta F-32\right)$$

Use the distributive property to multiply 10 by \theta F-32.

$$9GM-180=10\theta F-320$$

Add 180 to both sides.

$$9GM=10\theta F-320+180$$

Add -320 and 180 to get -140.

$$9GM=10\theta F-140$$

The equation is in standard form.

$$9MG=10F\theta -140$$

Divide both sides by 9M.

$$\frac{9MG}{9M}=\frac{10F\theta -140}{9M}$$

Dividing by 9M undoes the multiplication by 9M.

$$G=\frac{10F\theta -140}{9M}$$

Divide 10\theta F-140 by 9M.

$$G=\frac{10\left(F\theta -14\right)}{9M}$$

Solve for F

$$\left\{\begin{matrix}F=\frac{9GM+140}{10\theta }\text{, }&\theta \neq 0\\F\in \mathrm{R}\text{, }&G=-\frac{140}{9M}\text{ and }M\neq 0\text{ and }\theta =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 32 from 212 to get 180.

$$\frac{\theta F-32}{180}=\frac{GM-20}{220-20}$$

Subtract 20 from 220 to get 200.

$$\frac{\theta F-32}{180}=\frac{GM-20}{200}$$

Multiply both sides of the equation by 1800, the least common multiple of 180,200.

$$10\left(\theta F-32\right)=9\left(GM-20\right)$$

Use the distributive property to multiply 10 by \theta F-32.

$$10\theta F-320=9\left(GM-20\right)$$

Use the distributive property to multiply 9 by GM-20.

$$10\theta F-320=9GM-180$$

Add 320 to both sides.

$$10\theta F=9GM-180+320$$

Add -180 and 320 to get 140.

$$10\theta F=9GM+140$$

Divide both sides by 10\theta .

$$\frac{10\theta F}{10\theta }=\frac{9GM+140}{10\theta }$$

Dividing by 10\theta undoes the multiplication by 10\theta .

$$F=\frac{9GM+140}{10\theta }$$

Solve for G

$$\left\{\begin{matrix}G=-\frac{10\left(14-F\theta \right)}{9M}\text{, }&M\neq 0\\G\in \mathrm{R}\text{, }&\theta =\frac{14}{F}\text{ and }F\neq 0\text{ and }M=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 32 from 212 to get 180.

$$\frac{\theta F-32}{180}=\frac{GM-20}{220-20}$$

Subtract 20 from 220 to get 200.

$$\frac{\theta F-32}{180}=\frac{GM-20}{200}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{GM-20}{200}=\frac{\theta F-32}{180}$$

Multiply both sides of the equation by 1800, the least common multiple of 200,180.

$$9\left(GM-20\right)=10\left(\theta F-32\right)$$

Use the distributive property to multiply 9 by GM-20.

$$9GM-180=10\left(\theta F-32\right)$$

Use the distributive property to multiply 10 by \theta F-32.

$$9GM-180=10\theta F-320$$

Add 180 to both sides.

$$9GM=10\theta F-320+180$$

Add -320 and 180 to get -140.

$$9GM=10\theta F-140$$

The equation is in standard form.

$$9MG=10F\theta -140$$

Divide both sides by 9M.

$$\frac{9MG}{9M}=\frac{10F\theta -140}{9M}$$

Dividing by 9M undoes the multiplication by 9M.

$$G=\frac{10F\theta -140}{9M}$$

Divide 10\theta F-140 by 9M.

$$G=\frac{10\left(F\theta -14\right)}{9M}$$