Solve 4(A+B+C)=37(ABC)

$$4 ( A + B + C ) = 37 ( A B C )$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=-\frac{4\left(B+C\right)}{4-37BC}\text{, }&C=0\text{ or }B\neq \frac{4}{37C}\\A\in \mathrm{C}\text{, }&\left(B=-\frac{2\sqrt{37}i}{37}\text{ and }C=\frac{2\sqrt{37}i}{37}\right)\text{ or }\left(B=\frac{2\sqrt{37}i}{37}\text{ and }C=-\frac{2\sqrt{37}i}{37}\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by A+B+C.

$$4A+4B+4C=37ABC$$

Subtract 37ABC from both sides.

$$4A+4B+4C-37ABC=0$$

Subtract 4B from both sides. Anything subtracted from zero gives its negation.

$$4A+4C-37ABC=-4B$$

Subtract 4C from both sides.

$$4A-37ABC=-4B-4C$$

Combine all terms containing A.

$$\left(4-37BC\right)A=-4B-4C$$

Divide both sides by -37BC+4.

$$\frac{\left(4-37BC\right)A}{4-37BC}=\frac{-4B-4C}{4-37BC}$$

Dividing by -37BC+4 undoes the multiplication by -37BC+4.

$$A=\frac{-4B-4C}{4-37BC}$$

Divide -4B-4C by -37BC+4.

$$A=-\frac{4\left(B+C\right)}{4-37BC}$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B=-\frac{4\left(A+C\right)}{4-37AC}\text{, }&C=0\text{ or }A\neq \frac{4}{37C}\\B\in \mathrm{C}\text{, }&\left(A=-\frac{2\sqrt{37}i}{37}\text{ and }C=\frac{2\sqrt{37}i}{37}\right)\text{ or }\left(A=\frac{2\sqrt{37}i}{37}\text{ and }C=-\frac{2\sqrt{37}i}{37}\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by A+B+C.

$$4A+4B+4C=37ABC$$

Subtract 37ABC from both sides.

$$4A+4B+4C-37ABC=0$$

Subtract 4A from both sides. Anything subtracted from zero gives its negation.

$$4B+4C-37ABC=-4A$$

Subtract 4C from both sides.

$$4B-37ABC=-4A-4C$$

Combine all terms containing B.

$$\left(4-37AC\right)B=-4A-4C$$

Divide both sides by 4-37AC.

$$\frac{\left(4-37AC\right)B}{4-37AC}=\frac{-4A-4C}{4-37AC}$$

Dividing by 4-37AC undoes the multiplication by 4-37AC.

$$B=\frac{-4A-4C}{4-37AC}$$

Divide -4A-4C by 4-37AC.

$$B=-\frac{4\left(A+C\right)}{4-37AC}$$

Solve for A

$$A=-\frac{4\left(B+C\right)}{4-37BC}$$

$$C=0\text{ or }B\neq \frac{4}{37C}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by A+B+C.

$$4A+4B+4C=37ABC$$

Subtract 37ABC from both sides.

$$4A+4B+4C-37ABC=0$$

Subtract 4B from both sides. Anything subtracted from zero gives its negation.

$$4A+4C-37ABC=-4B$$

Subtract 4C from both sides.

$$4A-37ABC=-4B-4C$$

Combine all terms containing A.

$$\left(4-37BC\right)A=-4B-4C$$

Divide both sides by -37BC+4.

$$\frac{\left(4-37BC\right)A}{4-37BC}=\frac{-4B-4C}{4-37BC}$$

Dividing by -37BC+4 undoes the multiplication by -37BC+4.

$$A=\frac{-4B-4C}{4-37BC}$$

Divide -4B-4C by -37BC+4.

$$A=-\frac{4\left(B+C\right)}{4-37BC}$$

Solve for B

$$B=-\frac{4\left(A+C\right)}{4-37AC}$$

$$C=0\text{ or }A\neq \frac{4}{37C}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by A+B+C.

$$4A+4B+4C=37ABC$$

Subtract 37ABC from both sides.

$$4A+4B+4C-37ABC=0$$

Subtract 4A from both sides. Anything subtracted from zero gives its negation.

$$4B+4C-37ABC=-4A$$

Subtract 4C from both sides.

$$4B-37ABC=-4A-4C$$

Combine all terms containing B.

$$\left(4-37AC\right)B=-4A-4C$$

Divide both sides by 4-37AC.

$$\frac{\left(4-37AC\right)B}{4-37AC}=\frac{-4A-4C}{4-37AC}$$

Dividing by 4-37AC undoes the multiplication by 4-37AC.

$$B=\frac{-4A-4C}{4-37AC}$$

Divide -4A-4C by 4-37AC.

$$B=-\frac{4\left(A+C\right)}{4-37AC}$$