Solve 493/21A+493/12c=7419

$$\frac { 493 } { 21 A } + \frac { 493 } { 12 c } = 7419$$

Solve for A

$$A=-\frac{1972c}{7\left(493-89028c\right)}$$

$$c\neq 0\text{ and }c\neq \frac{493}{89028}$$

Steps for Solving Linear Equation

Variable A cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 84Ac, the least common multiple of 21A,12c.

$$4c\times 493+7A\times 493=623196Ac$$

Multiply 4 and 493 to get 1972.

$$1972c+7A\times 493=623196Ac$$

Multiply 7 and 493 to get 3451.

$$1972c+3451A=623196Ac$$

Subtract 623196Ac from both sides.

$$1972c+3451A-623196Ac=0$$

Subtract 1972c from both sides. Anything subtracted from zero gives its negation.

$$3451A-623196Ac=-1972c$$

Combine all terms containing A.

$$\left(3451-623196c\right)A=-1972c$$

Divide both sides by -623196c+3451.

$$\frac{\left(3451-623196c\right)A}{3451-623196c}=-\frac{1972c}{3451-623196c}$$

Dividing by -623196c+3451 undoes the multiplication by -623196c+3451.

$$A=-\frac{1972c}{3451-623196c}$$

Divide -1972c by -623196c+3451.

$$A=-\frac{1972c}{7\left(493-89028c\right)}$$

Variable A cannot be equal to 0.

$$A=-\frac{1972c}{7\left(493-89028c\right)}\text{, }A\neq 0$$

Solve for c

$$c=-\frac{3451A}{4\left(493-155799A\right)}$$

$$A\neq 0\text{ and }A\neq \frac{493}{155799}$$

Steps for Solving Linear Equation

Variable c cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 84Ac, the least common multiple of 21A,12c.

$$4c\times 493+7A\times 493=623196Ac$$

Multiply 4 and 493 to get 1972.

$$1972c+7A\times 493=623196Ac$$

Multiply 7 and 493 to get 3451.

$$1972c+3451A=623196Ac$$

Subtract 623196Ac from both sides.

$$1972c+3451A-623196Ac=0$$

Subtract 3451A from both sides. Anything subtracted from zero gives its negation.

$$1972c-623196Ac=-3451A$$

Combine all terms containing c.

$$\left(1972-623196A\right)c=-3451A$$

Divide both sides by -623196A+1972.

$$\frac{\left(1972-623196A\right)c}{1972-623196A}=-\frac{3451A}{1972-623196A}$$

Dividing by -623196A+1972 undoes the multiplication by -623196A+1972.

$$c=-\frac{3451A}{1972-623196A}$$

Divide -3451A by -623196A+1972.

$$c=-\frac{3451A}{4\left(493-155799A\right)}$$

Variable c cannot be equal to 0.

$$c=-\frac{3451A}{4\left(493-155799A\right)}\text{, }c\neq 0$$