Answer
$c=\dfrac{5}{2},\text{ }d=\dfrac{2}{5},\text{ }f=7,\text{ }g=5,\text{ }h=-1
$
Work Step by Step
Equating each corresponding elements in the given matrix equation, $
\begin{bmatrix}
4c & 2-d & 5
\\
-3 & -1 & 2
\\
0 & -10 & 15
\end{bmatrix}
=
\begin{bmatrix}
2c+5 & 4d & g
\\
-3 & h & f-g
\\
0 & -4c & 15
\end{bmatrix}
,$ and then solving the resulting equation, then
\begin{align*}
4c&=2c+5
\\
4c-2c&=2c-2c+5
\\
2c&=5
\\
\dfrac{2c}{2}&=\dfrac{5}{2}
\\
c&=\dfrac{5}{2}
,\\\\\\
2-d&=4d
\\
2-d+d&=4d+d
\\
2&=5d
\\
\dfrac{2}{5}&=\dfrac{5d}{5}
\\
\dfrac{2}{5}&=d
,\\\\\\
5&=g
,\\\\\\
-1&=h
,\\\\\\
2&=f-g
\\
2&=f-5
&\text{(substitute $g=5$)}
\\
2+5&=f-5+5
\\
7&=f
.\end{align*}
Hence, $
c=\dfrac{5}{2},\text{ }d=\dfrac{2}{5},\text{ }f=7,\text{ }g=5,\text{ }h=-1
.$
