32=(a+3)(a-1)

Solution for 32=(a+3)(a-1) equation:

32=(a+3)(a-1)

We move all terms to the left:

32-((a+3)(a-1))=0

We multiply parentheses ..

-((+a^2-1a+3a-3))+32=0


We calculate terms in parentheses: -((+a^2-1a+3a-3)), so:

(+a^2-1a+3a-3)

We get rid of parentheses

a^2-1a+3a-3

We add all the numbers together, and all the variables

a^2+2a-3

Back to the equation:

-(a^2+2a-3)


We get rid of parentheses

-a^2-2a+3+32=0

We add all the numbers together, and all the variables

-1a^2-2a+35=0

a = -1; b = -2; c = +35;
Δ = b2-4ac
Δ = -22-4·(-1)·35
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-12}{2*-1}=\frac{-10}{-2}
=+5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+12}{2*-1}=\frac{14}{-2}
=-7
$