Solve (x+4)^2=3(y-1)

$$( x + 4 ) ^ { 2 } = 3 ( y - 1 )$$

Solve for y

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

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$x^{2}+8x+16=3\left(y-1\right)$$

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

$$x^{2}+8x+16=3y-3$$

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

$$3y-3=x^{2}+8x+16$$

Add 3 to both sides.

$$3y=x^{2}+8x+16+3$$

Add 16 and 3 to get 19.

$$3y=x^{2}+8x+19$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{x^{2}+8x+19}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{x^{2}+8x+19}{3}$$

Solve for x (complex solution)

$$x=-\left(\sqrt{3\left(y-1\right)}+4\right)$$

$$x=\sqrt{3\left(y-1\right)}-4$$

Solve for x

$$x=-\left(\sqrt{3\left(y-1\right)}+4\right)$$

$$x=\sqrt{3\left(y-1\right)}-4\text{, }y\geq 1$$