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Math·Advanced Math·Equivalent expressions

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$f(x)=2x+3$

$g(x)=7x-2$

$h(x)=5x+6$

The functions $f$, $g$, and $h$ are defined as shown. If $f(x)\cdot g(x)-h(x)=a{x}^2+bx+c$, where $a$, $b$, and $c$ are constants, what is the value of $b$?

A

$-5$

B

$12$

C

$20$

D

$22$