Solve -(1+(y^2-4xz))/4x=37

$$- \frac{ (1+( { y }^{ 2 } -4xz)) }{ 4x } =37$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{y^{2}+1}{4\left(37-z\right)}\text{, }&y\neq -i\text{ and }y\neq i\text{ and }z\neq 37\\x\neq 0\text{, }&\left(y=i\text{ or }y=-i\right)\text{ and }z=37\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4x.

$$-\left(1+y^{2}-4xz\right)=148x$$

To find the opposite of 1+y^{2}-4xz, find the opposite of each term.

$$-1-y^{2}+4xz=148x$$

Subtract 148x from both sides.

$$-1-y^{2}+4xz-148x=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$-y^{2}+4xz-148x=1$$

Add y^{2} to both sides.

$$4xz-148x=1+y^{2}$$

Combine all terms containing x.

$$\left(4z-148\right)x=1+y^{2}$$

The equation is in standard form.

$$\left(4z-148\right)x=y^{2}+1$$

Divide both sides by 4z-148.

$$\frac{\left(4z-148\right)x}{4z-148}=\frac{y^{2}+1}{4z-148}$$

Dividing by 4z-148 undoes the multiplication by 4z-148.

$$x=\frac{y^{2}+1}{4z-148}$$

Divide 1+y^{2} by 4z-148.

$$x=\frac{y^{2}+1}{4\left(z-37\right)}$$

Variable x cannot be equal to 0.

$$x=\frac{y^{2}+1}{4\left(z-37\right)}\text{, }x\neq 0$$

Solve for x

$$x=-\frac{y^{2}+1}{4\left(37-z\right)}$$

$$z\neq 37$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4x.

$$-\left(1+y^{2}-4xz\right)=148x$$

To find the opposite of 1+y^{2}-4xz, find the opposite of each term.

$$-1-y^{2}+4xz=148x$$

Subtract 148x from both sides.

$$-1-y^{2}+4xz-148x=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$-y^{2}+4xz-148x=1$$

Add y^{2} to both sides.

$$4xz-148x=1+y^{2}$$

Combine all terms containing x.

$$\left(4z-148\right)x=1+y^{2}$$

The equation is in standard form.

$$\left(4z-148\right)x=y^{2}+1$$

Divide both sides by 4z-148.

$$\frac{\left(4z-148\right)x}{4z-148}=\frac{y^{2}+1}{4z-148}$$

Dividing by 4z-148 undoes the multiplication by 4z-148.

$$x=\frac{y^{2}+1}{4z-148}$$

Divide 1+y^{2} by 4z-148.

$$x=\frac{y^{2}+1}{4\left(z-37\right)}$$

Variable x cannot be equal to 0.

$$x=\frac{y^{2}+1}{4\left(z-37\right)}\text{, }x\neq 0$$

Solve for y (complex solution)

$$y=-\sqrt{4xz-148x-1}$$

$$y=\sqrt{4xz-148x-1}\text{, }x\neq 0$$

Solve for y

$$y=\sqrt{4xz-148x-1}$$

$$y=-\sqrt{4xz-148x-1}\text{, }\left(x\geq \frac{1}{4z-148}\text{ and }z>37\text{ and }x\neq 0\right)\text{ or }\left(x=\frac{1}{4z-148}\text{ and }z\neq 37\right)\text{ or }\left(z<37\text{ and }x\leq \frac{1}{4z-148}\text{ and }x\neq 0\right)$$