Answer :

Let's simplify the expression step by step:

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]

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