Solve 1/x+3*4y/2=12x^2

$$\frac { 1 } { x } + 3 \cdot \frac { 4 y } { 2 } = 12 x ^ { 2 }$$

Solve for y

$$y=2x^{2}-\frac{1}{6x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$2+3x\times 4y=12x^{2}\times 2x$$

Multiply 3 and 4 to get 12.

$$2+12xy=12x^{2}\times 2x$$

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

$$2+12xy=12x^{3}\times 2$$

Multiply 12 and 2 to get 24.

$$2+12xy=24x^{3}$$

Subtract 2 from both sides.

$$12xy=24x^{3}-2$$

Divide both sides by 12x.

$$\frac{12xy}{12x}=\frac{24x^{3}-2}{12x}$$

Dividing by 12x undoes the multiplication by 12x.

$$y=\frac{24x^{3}-2}{12x}$$

Divide 24x^{3}-2 by 12x.

$$y=2x^{2}-\frac{1}{6x}$$