Solve y=3(x+5)^2-3

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

Solve for y

$$y=3\left(x+4\right)\left(x+6\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$y=3\left(x^{2}+10x+25\right)-3$$

Use the distributive property to multiply 3 by x^{2}+10x+25.

$$y=3x^{2}+30x+75-3$$

Subtract 3 from 75 to get 72.

$$y=3x^{2}+30x+72$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{3y+9}}{3}-5$$

$$x=\frac{\sqrt{3y+9}}{3}-5$$

Solve for x

$$x=-\frac{\sqrt{3y+9}}{3}-5$$

$$x=\frac{\sqrt{3y+9}}{3}-5\text{, }y\geq -3$$