Simplify (3x-21)/(x^2-3x-28)*(5x+20)/(2x+8)

Factor ${\displaystyle 3}$ out of ${\displaystyle 3x}$.

Factor ${\displaystyle 3}$ out of ${\displaystyle -21}$.

Factor ${\displaystyle 3}$ out of ${\displaystyle 3x+3\cdot -7}$.

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle -28}$ and whose sum is ${\displaystyle -3}$.

Write the factored form using these integers.

Factor ${\displaystyle 5}$ out of ${\displaystyle 5x+20}$.

Factor ${\displaystyle 2}$ out of ${\displaystyle 2x+8}$.

Cancel the common factor of ${\displaystyle x+4}$.

Multiply ${\displaystyle \frac{3(x-7)}{x-7}}$ by ${\displaystyle \frac{5}{2(x+4)}}$.

Multiply ${\displaystyle 5}$ by ${\displaystyle 3}$.

Cancel the common factor of ${\displaystyle x-7}$.