Solve 2^2=x^2-3y(5z-1)

$${ 2 }^{ 2 } = { x }^{ 2 } -3y(5z-1)$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=-\frac{x^{2}-4}{3\left(1-5z\right)}\text{, }&z\neq \frac{1}{5}\\y\in \mathrm{C}\text{, }&\left(x=-2\text{ or }x=2\right)\text{ and }z=\frac{1}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 2 to the power of 2 and get 4.

$$4=x^{2}-3y\left(5z-1\right)$$

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

$$x^{2}-3y\left(5z-1\right)=4$$

Use the distributive property to multiply -3y by 5z-1.

$$x^{2}-15yz+3y=4$$

Subtract x^{2} from both sides.

$$-15yz+3y=4-x^{2}$$

Combine all terms containing y.

$$\left(-15z+3\right)y=4-x^{2}$$

The equation is in standard form.

$$\left(3-15z\right)y=4-x^{2}$$

Divide both sides by -15z+3.

$$\frac{\left(3-15z\right)y}{3-15z}=\frac{4-x^{2}}{3-15z}$$

Dividing by -15z+3 undoes the multiplication by -15z+3.

$$y=\frac{4-x^{2}}{3-15z}$$

Divide -x^{2}+4 by -15z+3.

$$y=\frac{\left(2-x\right)\left(x+2\right)}{3\left(1-5z\right)}$$

Solve for y

$$\left\{\begin{matrix}y=-\frac{x^{2}-4}{3\left(1-5z\right)}\text{, }&z\neq \frac{1}{5}\\y\in \mathrm{R}\text{, }&z=\frac{1}{5}\text{ and }|x|=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 2 to the power of 2 and get 4.

$$4=x^{2}-3y\left(5z-1\right)$$

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

$$x^{2}-3y\left(5z-1\right)=4$$

Use the distributive property to multiply -3y by 5z-1.

$$x^{2}-15yz+3y=4$$

Subtract x^{2} from both sides.

$$-15yz+3y=4-x^{2}$$

Combine all terms containing y.

$$\left(-15z+3\right)y=4-x^{2}$$

The equation is in standard form.

$$\left(3-15z\right)y=4-x^{2}$$

Divide both sides by -15z+3.

$$\frac{\left(3-15z\right)y}{3-15z}=\frac{4-x^{2}}{3-15z}$$

Dividing by -15z+3 undoes the multiplication by -15z+3.

$$y=\frac{4-x^{2}}{3-15z}$$

Divide -x^{2}+4 by -15z+3.

$$y=\frac{\left(2-x\right)\left(x+2\right)}{3\left(1-5z\right)}$$

Solve for x (complex solution)

$$x=-\sqrt{15yz-3y+4}$$

$$x=\sqrt{15yz-3y+4}$$

Solve for x

$$x=\sqrt{15yz-3y+4}$$

$$x=-\sqrt{15yz-3y+4}\text{, }\left(z\leq \frac{1}{5}\text{ or }y\geq -\frac{4}{15z-3}\right)\text{ and }\left(z\geq \frac{1}{5}\text{ or }y\leq -\frac{4}{15z-3}\right)$$