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^2-14a-21=0

a = 7; b = -14; c = -21;
Δ = b2-4ac
Δ = -142-4·7·(-21)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-28}{2*7}=\frac{-14}{14}
=-1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+28}{2*7}=\frac{42}{14}
=3
$