Solve 2y=4z(z+x)+x^2+3

$$2y=4z(z+x)+ { x }^{ 2 } +3$$

Solve for y

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

Steps for Solving Linear Equation

Use the distributive property to multiply 4z by z+x.

$$2y=4z^{2}+4zx+x^{2}+3$$

The equation is in standard form.

$$2y=x^{2}+4xz+4z^{2}+3$$

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Solve for x (complex solution)

$$x=-2z+\sqrt{2y-3}$$

$$x=-2z-\sqrt{2y-3}$$

Solve for x

$$x=-2z+\sqrt{2y-3}$$

$$x=-2z-\sqrt{2y-3}\text{, }y\geq \frac{3}{2}$$