Solve 8(2/3-3a^2/2)/24c=44

$$\frac { 8 ( \frac { 2 } { 3 } - \frac { 3 a ^ { 2 } } { 2 } ) } { 24 c } = 44$$

Solve for c

$$c=-\frac{a^{2}}{88}+\frac{1}{198}$$

$$|a|\neq \frac{2}{3}$$

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 24c.

$$8\left(\frac{2}{3}-\frac{3a^{2}}{2}\right)=1056c$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{2}{3} times \frac{2}{2}. Multiply \frac{3a^{2}}{2} times \frac{3}{3}.

$$8\left(\frac{2\times 2}{6}-\frac{3\times 3a^{2}}{6}\right)=1056c$$

Since \frac{2\times 2}{6} and \frac{3\times 3a^{2}}{6} have the same denominator, subtract them by subtracting their numerators.

$$8\times \frac{2\times 2-3\times 3a^{2}}{6}=1056c$$

Do the multiplications in 2\times 2-3\times 3a^{2}.

$$8\times \frac{4-9a^{2}}{6}=1056c$$

Express 8\times \frac{4-9a^{2}}{6} as a single fraction.

$$\frac{8\left(4-9a^{2}\right)}{6}=1056c$$

Use the distributive property to multiply 8 by 4-9a^{2}.

$$\frac{32-72a^{2}}{6}=1056c$$

Divide each term of 32-72a^{2} by 6 to get \frac{16}{3}-12a^{2}.

$$\frac{16}{3}-12a^{2}=1056c$$

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

$$1056c=\frac{16}{3}-12a^{2}$$

Divide both sides by 1056.

$$\frac{1056c}{1056}=\frac{\frac{16}{3}-12a^{2}}{1056}$$

Dividing by 1056 undoes the multiplication by 1056.

$$c=\frac{\frac{16}{3}-12a^{2}}{1056}$$

Divide -12a^{2}+\frac{16}{3} by 1056.

$$c=-\frac{a^{2}}{88}+\frac{1}{198}$$

Variable c cannot be equal to 0.

$$c=-\frac{a^{2}}{88}+\frac{1}{198}\text{, }c\neq 0$$

Solve for a

$$a=\frac{2\sqrt{1-198c}}{3}$$

$$a=-\frac{2\sqrt{1-198c}}{3}\text{, }c\leq \frac{1}{198}\text{ and }c\neq 0$$