Answer
$ h= -1.5\ ,\quad h= 7$
Work Step by Step
Let's first simplify a bit before factoring.$$
\begin{aligned}
55+55 h&=10 h^2-50 \\
10 h^2-55 h-50-55& =0\\
10 h^2-55 h-105& =0\\
5\left( 2h^2-11h-21\right)&= 0\\
2h^2-11h-21&= 0.
\end{aligned}
$$ We can now factor this simplified version, $ 2h^2-11h-21= 0$. Now, multiply: $2\cdot (-21) = -42$, and the find two numbers that when multiplied, you get $-42$, and when added, you get $-11$. The two numbers that will do are $-14$ and $3$.
$$
\begin{aligned}
2h^2-11h-21&= 0\\
2h^2-14h+3h-21&= 0\\
2h(h-7)+3(h-7)&= 0\\
(h-7)(2h+3)&= 0.
\end{aligned}
$$ Hence, $$
\begin{aligned}
h-7&= 0\\
h&= 7\\
2h+3&= 0\\
2h&= -3\\
h&= -\frac{3}{2}\\
&= -1.5
\end{aligned}
$$ Check $$
\begin{aligned}
55+55 \cdot(7)&\stackrel{?}{=}10\cdot 7^2-50 \\
440& =440\checkmark\\
55+55 \cdot(-1.5)&\stackrel{?}{=}10\cdot (-1.5)^2-50 \\
-27.5& =-27.5\checkmark.
\end{aligned}
$$
