First step is to separate the terms with variables from the constant terms.
Add 13 to both sides of the equation :
[tex]\begin{gathered} 6x^2+96x-13=-13 \\ 6x^2+96x-\cancel{13}+\cancel{13}=-13+13 \\ 6x^2+96x=0 \end{gathered}[/tex]Divide both sides by 6 :
[tex]\begin{gathered} 6x^2+96x=0 \\ x^2+16x=0 \end{gathered}[/tex]Next step, completing the square by adding this term to both sides of the equation :
[tex](\frac{b}{2a})^2[/tex]From the equation,
a = 1
b = 16
So it follows that :
[tex](\frac{b}{2a})^2=(\frac{16}{2\times1})^2=(8)^2[/tex]Adding this to both sides of the equation :
[tex]\begin{gathered} x^2+16x=0 \\ x^2+16x+8^2=8^2 \end{gathered}[/tex]And you will get a perfect square trinomial on the left side of the equation in the form :
[tex]x^2+bx+c^2[/tex]It can be factored as :
[tex]x^2+bx+c^2=(x+c)^2[/tex]So the equation will be :
[tex]\begin{gathered} x^2+16x+8^2=8^2 \\ (x+8)^2=8^2 \\ (x+8)^2=64 \end{gathered}[/tex]The answer is :
[tex](x+8)^2=64[/tex]