7(-a-1)*(-a-3)=0

Solution for 7(-a-1)*(-a-3)=0 equation:

7(-a-1)(-a-3)=0

We add all the numbers together, and all the variables

7(-1a-1)(-1a-3)=0

We multiply parentheses ..

7(+a^2+3a+a+3)=0

We multiply parentheses

7a^2+21a+7a+21=0

We add all the numbers together, and all the variables

7a^2+28a+21=0

a = 7; b = 28; c = +21;
Δ = b2-4ac
Δ = 282-4·7·21
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-14}{2*7}=\frac{-42}{14}
=-3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+14}{2*7}=\frac{-14}{14}
=-1
$