To determine how far the firework will travel before it reaches the ground, we need to solve the equation \( h(x) = 0 \), where \( h(x) \) is the height of the firework given by the equation:
\[ h(x) = -x^2 + 15x \]
Setting \( h(x) \) equal to zero, we have:
\[ 0 = -x^2 + 15x \]
We can rearrange this equation to make it easier to solve:
\[ x^2 - 15x = 0 \]
Next, we factor the equation:
\[ x(x - 15) = 0 \]
Setting each factor equal to zero gives us:
- \( x = 0 \)
- \( x - 15 = 0 \) which simplifies to \( x = 15 \)
The solutions to the equation are \( x = 0 \) and \( x = 15 \). Since \( x = 0 \) represents the starting point (when the firework is launched), the distance the firework travels before it reaches the ground is:
\[ \boxed{15} \text{ feet} \]