Solve 3/4x*1/2x*5/6x=y/2

$$\frac { 3 } { 4 x } \cdot \frac { 1 } { 2 x } \cdot \frac { 5 } { 6 x } = \frac { y } { 2 }$$

Solve for y

$$y=\frac{5}{8x^{3}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12x, the least common multiple of 4x,2x,6x,2.

$$3\times 3\times \frac{1}{2x}\times \frac{5}{6x}=6xy$$

Multiply 3 and 3 to get 9.

$$9\times \frac{1}{2x}\times \frac{5}{6x}=6xy$$

Express 9\times \frac{1}{2x} as a single fraction.

$$\frac{9}{2x}\times \frac{5}{6x}=6xy$$

Multiply \frac{9}{2x} times \frac{5}{6x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 5}{2x\times 6x}=6xy$$

Cancel out 3 in both numerator and denominator.

$$\frac{3\times 5}{2\times 2xx}=6xy$$

Multiply x and x to get x^{2}.

$$\frac{3\times 5}{2\times 2x^{2}}=6xy$$

Multiply 3 and 5 to get 15.

$$\frac{15}{2\times 2x^{2}}=6xy$$

Multiply 2 and 2 to get 4.

$$\frac{15}{4x^{2}}=6xy$$

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

$$6xy=\frac{15}{4x^{2}}$$

Multiply both sides of the equation by 4x^{2}.

$$6xy\times 4x^{2}=15$$

Reorder the terms.

$$4\times 6xyx^{2}=15$$

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

$$4\times 6x^{3}y=15$$

Multiply 4 and 6 to get 24.

$$24x^{3}y=15$$

Divide both sides by 24x^{3}.

$$\frac{24x^{3}y}{24x^{3}}=\frac{15}{24x^{3}}$$

Dividing by 24x^{3} undoes the multiplication by 24x^{3}.

$$y=\frac{15}{24x^{3}}$$

Divide 15 by 24x^{3}.

$$y=\frac{5}{8x^{3}}$$

Solve for x (complex solution)

$$x=\frac{\sqrt[3]{5}e^{\frac{2\pi i}{3}}y^{-\frac{1}{3}}}{2}$$

$$x=\frac{\sqrt[3]{5}y^{-\frac{1}{3}}}{2}$$

$$x=\frac{\sqrt[3]{5}e^{\frac{4\pi i}{3}}y^{-\frac{1}{3}}}{2}\text{, }y\neq 0$$

Solve for x

$$x=\frac{\sqrt[3]{\frac{5}{y}}}{2}$$

$$y\neq 0$$