To solve the expression $6x + x^2 - 5$ when $x = 3$, we simply substitute the value of $x$ into the equation and simplify.

1. Substitute $x = 3$ into the expression:

$6(3) + 3^2 - 5$

2. Now, calculate each term:

$6(3) = 18$ $3^2 = 9$

So the expression becomes:

$18 + 9 - 5$

3. Simplify further:

$18 + 9 = 27$ $27 - 5 = 22$

Thus, the value of the expression is $22$.

Would you like more details on any of the steps?

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Here are 5 related questions to explore further:

1. How would the result change if $x = -3$?
2. What is the result of the expression $x^2 - 6x + 5$ when $x = 3$?
3. How would you factor the expression $x^2 + 6x - 5$?
4. What is the derivative of the expression $6x + x^2 - 5$?
5. How does the value of the expression change if $x = 0$?

Tip: Always simplify expressions step by step, handling multiplication, powers, and then addition/subtraction carefully.