Partial Fraction Simplification

[tmt1]

I have this partial fraction:

$$ 18 = (x^2 + 9) + (Bx + C)(x + 3)$$

which the textbook says is equal to:

$$(B + 1)x^2 + (C + 3B)x + (9 + 3C)$$

But I don't follow this step. How do I derive this?

 

[MarkFL]

Okay, we begin with:

$$\left(x^2+9\right)+(Bx+C)(x+3)$$

What to you get when you carry out the indicated multiplication of the two binomial expressions?