Solve 3x^2y/2z=/4x^2z

$$\frac { 3 x ^ { 2 } y } { 2 z } = \frac { } { 4 x ^ { 2 } z }$$

Solve for y

$$y=\frac{1}{6x^{4}}$$

$$z\neq 0\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4zx^{2}, the least common multiple of 2z,4x^{2}z.

$$2x^{2}\times 3x^{2}y=1$$

Multiply 2 and 3 to get 6.

$$6x^{2}x^{2}y=1$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$6x^{4}y=1$$

Divide both sides by 6x^{4}.

$$\frac{6x^{4}y}{6x^{4}}=\frac{1}{6x^{4}}$$

Dividing by 6x^{4} undoes the multiplication by 6x^{4}.

$$y=\frac{1}{6x^{4}}$$

Solve for x

$$x=-\frac{6^{\frac{3}{4}}}{6\sqrt[4]{y}}$$

$$x=\frac{6^{\frac{3}{4}}}{6\sqrt[4]{y}}\text{, }y>0\text{ and }z\neq 0$$