(p+3)(p-5)=2p+6

Solution for (p+3)(p-5)=2p+6 equation:

(p+3)(p-5)=2p+6

We move all terms to the left:

(p+3)(p-5)-(2p+6)=0

We get rid of parentheses

(p+3)(p-5)-2p-6=0

We multiply parentheses ..

(+p^2-5p+3p-15)-2p-6=0

We get rid of parentheses

p^2-5p+3p-2p-15-6=0

We add all the numbers together, and all the variables

p^2-4p-21=0

a = 1; b = -4; c = -21;
Δ = b2-4ac
Δ = -42-4·1·(-21)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-10}{2*1}=\frac{-6}{2}
=-3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10}{2*1}=\frac{14}{2}
=7
$