Solve 5c^2/6ab*3b/a^2c=1

$$\frac { 5 c ^ { 2 } } { 6 a b } \cdot \frac { 3 b } { a ^ { 2 } c } = 1$$

Solve for b

$$b\neq 0$$

$$c\neq 0\text{ and }a=\frac{2^{\frac{2}{3}}\sqrt[3]{5c}}{2}$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6bca^{2}, the least common multiple of 6ab,a^{2}c.

$$ca\times 5c^{2}\times \frac{3b}{a^{2}c}=6bca^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$c^{3}a\times 5\times \frac{3b}{a^{2}c}=6bca^{2}$$

Express c^{3}\times \frac{3b}{a^{2}c} as a single fraction.

$$\frac{c^{3}\times 3b}{a^{2}c}a\times 5=6bca^{2}$$

Cancel out c in both numerator and denominator.

$$\frac{3bc^{2}}{a^{2}}a\times 5=6bca^{2}$$

Express \frac{3bc^{2}}{a^{2}}a as a single fraction.

$$\frac{3bc^{2}a}{a^{2}}\times 5=6bca^{2}$$

Cancel out a in both numerator and denominator.

$$\frac{3bc^{2}}{a}\times 5=6bca^{2}$$

Express \frac{3bc^{2}}{a}\times 5 as a single fraction.

$$\frac{3bc^{2}\times 5}{a}=6bca^{2}$$

Subtract 6bca^{2} from both sides.

$$\frac{3bc^{2}\times 5}{a}-6bca^{2}=0$$

Multiply 3 and 5 to get 15.

$$\frac{15bc^{2}}{a}-6bca^{2}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6bca^{2} times \frac{a}{a}.

$$\frac{15bc^{2}}{a}-\frac{6bca^{2}a}{a}=0$$

Since \frac{15bc^{2}}{a} and \frac{6bca^{2}a}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15bc^{2}-6bca^{2}a}{a}=0$$

Do the multiplications in 15bc^{2}-6bca^{2}a.

$$\frac{15bc^{2}-6bca^{3}}{a}=0$$

Multiply both sides of the equation by a.

$$15bc^{2}-6bca^{3}=0$$

Combine all terms containing b.

$$\left(15c^{2}-6ca^{3}\right)b=0$$

Divide 0 by 15c^{2}-6ca^{3}.

$$b=0$$

Variable b cannot be equal to 0.

$$b\in \emptyset$$

Solve for a

$$a=\frac{2^{\frac{2}{3}}\sqrt[3]{5c}}{2}$$

$$b\neq 0\text{ and }c\neq 0$$