Answer
$x = - \frac{5}{2}$ and $x = 9$
Work Step by Step
To find the $x$-intercepts we substitute $y=0$ in the equation: $$\begin{align*}
y&=(2x+5)(x-9)^2&&\text{Write equation.}\\
0&=(2x+5)(x-9)^2&&\text{Substitute }0\text{ for }y.\\
2x+5&=0\text{ or }(x-9)^2=0&&\text{Zero-Product Property.}\\
x&=-\frac{5}{2}\text{ or }x=9&&\text{Solve for }x.
\end{align*}$$ So there are two $x$-intercepts: $$x=-\frac{5}{2}\text{ and }x=9,$$ where $x=9$ has multiplicity $2$. This means that the curve crosses the $x$-axis at $x=-\frac{5}{2}$ and touches it at $x=9$.
