The problem asks to simplify the expression $3(x + 5) - x(x - 2)$.

1. Problem Description

The problem asks to simplify the expression $3(x + 5) - x(x - 2)$.

2. Solution Steps

First, distribute the $3$ in the first term:

$3(x + 5) = 3x + 15$

Next, distribute the $-x$ in the second term:

$-x(x - 2) = -x^2 + 2x$

Now, combine the two resulting expressions:

$3x + 15 - x^2 + 2x$

Combine like terms:

$-x^2 + (3x + 2x) + 15 = -x^2 + 5x + 15$

3. Final Answer

$-x^2 + 5x + 15$