## Answer :

Given:

[tex]\[ \left(-v^2 + 5v - 6\right) + \left(v^2 + 7v\right) \][/tex]

**Step 1: Combine like terms**

First, let's group the terms involving [tex]\( v^2 \)[/tex], [tex]\( v \)[/tex], and the constant terms separately:

- Terms involving [tex]\( v^2 \)[/tex]:

[tex]\[ -v^2 + v^2 \][/tex]

- Terms involving [tex]\( v \)[/tex]:

[tex]\[ 5v + 7v \][/tex]

- Constant terms:

[tex]\[ -6 \][/tex]

**Step 2: Simplify each group**

Now, let's simplify each group of terms:

- The [tex]\( v^2 \)[/tex] terms:

[tex]\[ -v^2 + v^2 = 0 \][/tex]

- The [tex]\( v \)[/tex] terms:

[tex]\[ 5v + 7v = 12v \][/tex]

- The constant term remains the same:

[tex]\[ -6 \][/tex]

**Step 3: Combine the simplified terms**

Combining the simplified terms, we get:

[tex]\[ 0 + 12v -6 \][/tex]

Since [tex]\( 0 \)[/tex] does not affect the expression, the simplified expression becomes:

[tex]\[ 12v - 6 \][/tex]

Therefore, the simplified expression is:

[tex]\[ \boxed{12v - 6} \][/tex]