(p+7)(p+3)=-3

Solution for (p+7)(p+3)=-3 equation:

(p+7)(p+3)=-3

We move all terms to the left:

(p+7)(p+3)-(-3)=0

We add all the numbers together, and all the variables

(p+7)(p+3)+3=0

We multiply parentheses ..

(+p^2+3p+7p+21)+3=0

We get rid of parentheses

p^2+3p+7p+21+3=0

We add all the numbers together, and all the variables

p^2+10p+24=0

a = 1; b = 10; c = +24;
Δ = b2-4ac
Δ = 102-4·1·24
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2}{2*1}=\frac{-12}{2}
=-6
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2}{2*1}=\frac{-8}{2}
=-4
$