To rewrite the given equation [tex]\(6(x+5)^2 + 5(x+5) - 4 = 0\)[/tex] as a quadratic equation, we can use a substitution. The goal of the substitution is to simplify the expression into a standard quadratic form.
Let's examine the given equation:
[tex]\[ 6(x+5)^2 + 5(x+5) - 4 = 0 \][/tex]
We notice that the expression [tex]\(x+5\)[/tex] appears in both the quadratic term and the linear term. To simplify this, we can introduce a new variable [tex]\(u\)[/tex]. We set:
[tex]\[ u = (x+5) \][/tex]
With this substitution, the equation becomes:
[tex]\[ 6u^2 + 5u - 4 = 0 \][/tex]
Now, we have rewritten the original equation in the standard quadratic form using the substitution [tex]\(u = (x+5)\)[/tex].
So, the correct substitution to rewrite the original equation as a quadratic equation is:
[tex]\[ u = (x+5) \][/tex]
Therefore, the correct choice is:
[tex]\[ u = (x+5) \][/tex]
