Solve ((x+y^2)-42/(2x)(y))*12=5

$$( \frac{ (x+ { y }^{ 2 } )-42 }{ (2x)(y) } ) \times 12=5$$

Solve for x (complex solution)

$$x=-\frac{6\left(y^{2}-42\right)}{6-5y}$$

$$y\neq -\sqrt{42}\text{ and }y\neq \sqrt{42}\text{ and }y\neq \frac{6}{5}\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Divide both sides by 12.

$$\frac{x+y^{2}-42}{2xy}=\frac{5}{12}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12xy, the least common multiple of 2xy,12.

$$6\left(x+y^{2}-42\right)=5xy$$

Use the distributive property to multiply 6 by x+y^{2}-42.

$$6x+6y^{2}-252=5xy$$

Subtract 5xy from both sides.

$$6x+6y^{2}-252-5xy=0$$

Subtract 6y^{2} from both sides. Anything subtracted from zero gives its negation.

$$6x-252-5xy=-6y^{2}$$

Add 252 to both sides.

$$6x-5xy=-6y^{2}+252$$

Combine all terms containing x.

$$\left(6-5y\right)x=-6y^{2}+252$$

The equation is in standard form.

$$\left(6-5y\right)x=252-6y^{2}$$

Divide both sides by 6-5y.

$$\frac{\left(6-5y\right)x}{6-5y}=\frac{252-6y^{2}}{6-5y}$$

Dividing by 6-5y undoes the multiplication by 6-5y.

$$x=\frac{252-6y^{2}}{6-5y}$$

Divide -6y^{2}+252 by 6-5y.

$$x=\frac{6\left(42-y^{2}\right)}{6-5y}$$

Variable x cannot be equal to 0.

$$x=\frac{6\left(42-y^{2}\right)}{6-5y}\text{, }x\neq 0$$

Solve for x

$$x=-\frac{6\left(y^{2}-42\right)}{6-5y}$$

$$y\neq \frac{6}{5}\text{ and }y\neq 0\text{ and }|y|\neq \sqrt{42}$$

Steps for Solving Linear Equation

Divide both sides by 12.

$$\frac{x+y^{2}-42}{2xy}=\frac{5}{12}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12xy, the least common multiple of 2xy,12.

$$6\left(x+y^{2}-42\right)=5xy$$

Use the distributive property to multiply 6 by x+y^{2}-42.

$$6x+6y^{2}-252=5xy$$

Subtract 5xy from both sides.

$$6x+6y^{2}-252-5xy=0$$

Subtract 6y^{2} from both sides. Anything subtracted from zero gives its negation.

$$6x-252-5xy=-6y^{2}$$

Add 252 to both sides.

$$6x-5xy=-6y^{2}+252$$

Combine all terms containing x.

$$\left(6-5y\right)x=-6y^{2}+252$$

The equation is in standard form.

$$\left(6-5y\right)x=252-6y^{2}$$

Divide both sides by 6-5y.

$$\frac{\left(6-5y\right)x}{6-5y}=\frac{252-6y^{2}}{6-5y}$$

Dividing by 6-5y undoes the multiplication by 6-5y.

$$x=\frac{252-6y^{2}}{6-5y}$$

Divide -6y^{2}+252 by 6-5y.

$$x=\frac{6\left(42-y^{2}\right)}{6-5y}$$

Variable x cannot be equal to 0.

$$x=\frac{6\left(42-y^{2}\right)}{6-5y}\text{, }x\neq 0$$

Solve for y

$$\left\{\begin{matrix}y=\frac{-\sqrt{25x^{2}-144x+6048}+5x}{12}\text{, }&x\neq 42\text{ and }x\neq 0\\y=\frac{\sqrt{25x^{2}-144x+6048}+5x}{12}\text{, }&x\neq 0\end{matrix}\right.$$